Find each difference in the photo below

Answer:

1. H0 : p = 0.9

   H1 : p ≠ 0.9

2. The test is two tailed.

3. Reject the null hypothesis

Step-by-step explanation:

We are given that we have to test the claim that the proportion of people who own cats is significantly different than 90% at the 0.1 significance level.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.90

Alternate Hypothesis, [tex]H_1[/tex] : p [tex]\neq[/tex] 0.9

Here, the test is two tailed because we have given that to test  the claim that the proportion of people who own cats is significantly different than 90% which means it can be less than 0.90 or more than 0.90.

Now, test statistics is given by;

            [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)   , where,  n = sample size = 100

                                                       [tex]\hat p[/tex] = 0.94 (given)

So, Test statistics = [tex]\frac{0.94-0.90}{\sqrt{\frac{0.94(1-0.94)}{100} } }[/tex] = 1.68

Now, P-value = P(Z > 1.68) = 1 - P(Z <= 1.68)

                                           = 1 - 0.95352 = 0.0465 ≈ 0.05 or 5%

Now, our decision rule is that;

       If p-value < significance level  ⇒ Reject null hypothesis

       If p-value > significance level  ⇒ Accept null hypothesis

Since, here p-value is less than significance level as 0.05 < 0.1, so we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that proportion of people who own cats is significantly different than 90%.

Answer:

The answer is c. The expected value.

Step-by-step explanation:

Final answer:

The weighted average of the value of a random variable calculated with probability weights is known as the expected value. The expected value indicates the long-term average outcome for a random variable that has been experimented on multiple times. It is calculated using the sum of the products of the variable values and their corresponding probabilities.

Explanation:

The weighted average of the value of a random variable, where the probability function provides weights, is known as the expected value. The expected value is a key concept in probability and statistics, often referred to in equations as E(X) and symbolized as μ (mu), where X is a random variable. It represents the long-term average outcome of a random variable after many repetitions of an experiment. For a discrete random variable with a probability distribution function P(x), the expected value can be calculated using the formula: μ = Σ XP(x).

Random variables are typically defined in the context of a probability distribution, which can take on various forms like normal, uniform, or exponential distributions, depending on the nature of the experiment. When constructing a confidence interval for a population mean, the confidence level indicates the degree of certainty in the interval estimate. The error bound, which is part of the confidence interval calculation, would typically decrease if the confidence level is lowered because a lower confidence level means that we are willing to accept a greater chance that the interval does not contain the population mean, leading to a narrower interval.

Answer:

a. First four terms of the sequential partial sums

[tex]S_1=\frac{1}{7}, S_2=\frac{7^2-1}{6*7^2}, S_3 =\frac{7^3-1}{6*7^3}, S_4 =\frac{7^4-1}{6*7^4}[/tex]

b. The formula for Sn is option A = [tex]\frac{7^n-1}{6*7^n}[/tex]

c. Value of the series = [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

a. First four terms of the sequential partial sums

[tex]\sum^{\infty}_{k=1}\\S_1=\frac{1}{7}\\ S_2=\frac{1}{7}+ \frac{1}{7^2}= \frac{8}{49} =\frac{7^2-1}{6*7^2}\\S_3=\frac{1}{7}+ \frac{1}{7^2}+\frac{1}{7^3} = \frac{57}{343} =\frac{7^3-1}{6*7^3}\\S_4=\frac{1}{7}+ \frac{1}{7^2}+\frac{1}{7^3}+\frac{1}{7^4} = \frac{400}{2401} =\frac{7^4-1}{6*7^4}[/tex]

b. Formula for Sn

The sum of n terms

[tex]S_n=\frac{1}{7}+ \frac{1}{7^2}+\frac{1}{7^3}+ \frac{1}{7^4}+.....+ \frac{1}{7^n}= \frac{7^n-1}{6*7^n}[/tex]

c. Value for the series

This can be given as the Sum of infinite terms;

[tex]S_{\infty}=\frac{1}{7}+ \frac{1}{7^2}+ \frac{1}{7^3}+ \frac{1}{7^4}+....+ \frac{1}{7^n}+ ....= \lim_{n \to \infty} \frac{7^n-1}{6*7^n}= \frac{1}{6}[/tex]

Answer:

100% probability that between 1200 and 1450 of those surveyed incurred debt.

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 2500, p = 0.52[/tex]

So

[tex]\mu = E(X) = 2500*0.52 = 1300[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2500*0.52*0.48} = 24.98[/tex]

Determine the probability that between 1200 and 1450 of those surveyed incurred debt.

This is the pvalue of Z when X = 1450 subtracted by the pvalue of Z when X = 1200. So

X = 1450

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1450 - 1300}{24.98}[/tex]

[tex]Z = 6[/tex]

[tex]Z = 6[/tex] has a pvalue of 1

X = 1200

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1200 - 1300}{24.98}[/tex]

[tex]Z = -4[/tex]

[tex]Z = -4[/tex] has a pvalue of 0

1 - 0 = 1

100% probability that between 1200 and 1450 of those surveyed incurred debt.

Answer:

(5.216) mean = 61.71

(5.217) standard deviation = 8.88

(5.218) P(X>=60) = 0.9238

(5.129) L = 79, U = 69

(5.130) P(X> or = U) = 0.7058

Step-by-step explanation:

The table of the statistic is set up as shown in attachment.

(5.216) mean = summation of all X ÷ no of data.

mean = 432/7 = 61.71 birds

(5.217)Standard deviation = √ sum of the absolute value of difference of X from mean ÷ number of data

S = √ /X - mean/ ÷ 7

= √551.428/7

S = 8.88

(5.218) P (X> or = 60)

= P(Z> or =60 - 61.71/8.8 )

= P(Z>or= - 0.192)

= 1 - P(Z< or = 0.192)

= 1- 0.0762

= 0.9238

(5.219)the 15th percentile=15/100 × 7

15th percentile = 1.05

The value is the number in the first position and that is 79,

L= 79

85th percentile = 85/100 × 7 = 5.95

The value is the number in the 6th position, and that is 69

U = 69

5.130) P(X>or = 60)

= P(Z>or= 69 - 61.71/8.8)

= P(Z> or = 0.8208)

= 1 - P(Z< or = 0.8209)

= 1 - 0.2942

= 0.7058

Answer:

At 0.05 level of significance, there is no difference in the mean number of larvae per stem. This supports the scientist's claim.

(d) H0: MeanMalathion - MeanNoMalathion equals 0

H1: MeanMalathion - MeanNoMalathion not equals 0

Step-by-step explanation:

Test statistic (t) = (mean 1 - mean 2) ÷ sqrt[pooled variance (1/n1 + 1/n2)]

Let the difference between the two means be x and the pooled variance be y

n1 = 5, n2 = 12

t = x ÷ sqrt[y(1/5 + 1/12)] = x ÷ sqrt(0.283y) = x ÷ 0.532√y = 1.88x/√y

Assuming the ratio of x to √y is 0.5

t = 1.88×0.5 = 0.94

n1 + n2 = 5 + 12 = 17

degree of freedom = n1 + n2 - 2 = 17 - 2 = 15

significance level = 0.05 = 5%

critical value corresponding to 15 degrees of freedom and 5% confidence interval is 2.131

The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

The region of no rejection of the null hypothesis lies between -2.131 and 2.131

Conclusion

Fail to reject the null hypothesis because the test statistic 0.94 falls within the region bounded by the critical values.

The scientist's claim is right.

A null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.

An alternate hypothesis is also a statement from a population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.

Answer:

a. Should NOT be rejected because all the parameters are generally acceptable.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

We are interested on this probability

[tex]P(X<\mu -2\sigma = 36.6 -2*1.2 =34.2)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<34.2)=P(\frac{X-\mu}{\sigma}<\frac{34.2-\mu}{\sigma})=P(Z<\frac{34.2-36.6}{1.2})=P(z<-2)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-2)=0.025[/tex]

And the best answer for this case would be:

2.5%

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the head circumference of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(36.6,1.2)[/tex]  

Where [tex]\mu=36.6[/tex] and [tex]\sigma=1.2[/tex]

We are interested on this probability

[tex]P(X<\mu -2\sigma = 36.6 -2*1.2 =34.2)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<34.2)=P(\frac{X-\mu}{\sigma}<\frac{34.2-\mu}{\sigma})=P(Z<\frac{34.2-36.6}{1.2})=P(z<-2)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-2)=0.025[/tex]

And the best answer for this case would be:

2.5%

Answer:

[tex]z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015[/tex]  

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

[tex]\hat p=0.3[/tex] estimated proportion of interest

[tex]p_o=0.45[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.45.:  

Null hypothesis:[tex]p=0.45[/tex]  

Alternative hypothesis:[tex]p \neq 0.45[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.3 -0.45}{\sqrt{\frac{0.45(1-0.45)}{100}}}=-3.015[/tex]  

The z-value is approximately -3.01.

To test the null hypothesis about a population proportion, you can use the z-test for proportions. The formula for the z-test statistic for proportions is:

[tex]z= \frac{p -p_0}{\frac{\sqrt{p_0(1 -p_0)}}{n} }[/tex]

​where:

p  is the sample proportion,  

p_0 is the hypothesized population proportion under the null hypothesis, n is the sample size.

In your case:

p =0.30 (sample proportion),

p_0​ =0.45 (hypothesized population proportion),

n=100 (sample size).

Now plug these values into the formula:

Calculate the values within the brackets first:

[tex]z= \frac{0.30 - 0.45}{\frac{\sqrt{0.45(1 -0.45)}}{100} }[/tex]

[tex]z= \frac{-0.15}{\frac{\sqrt{0.45(0.55)}}{100} }[/tex]

[tex]z= \frac{-0.15}{\frac{\sqrt{0.2475}}{100} }[/tex]

[tex]z= \frac{-0.15}{\sqrt{0.002475} }[/tex]

z≈−3.01

So, the z-value is approximately -3.01.

for such more question on null hypothesis

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Answer:

See the attached picture.

Step-by-step explanation:

See the attached picture.

To ensure compositions f ∘ g, g ∘ f, and f ∘ f make sense, certain conditions must be met regarding the number of inputs and outputs of the functions.

(a) For f ∘ g to make sense, the number of inputs of g must match the number of outputs of f. Therefore, n must equal p, and m must equal q.

(b) For g ∘ f to make sense, the number of inputs of f must match the number of outputs of g. Therefore, n must equal q, and m must equal p.

(c) For f ∘ f to make sense, the number of outputs of f must match the number of inputs of f. Therefore, n must equal m.

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Answer:

Option C.  failing to reject a false null hypothesis

Step-by-step explanation:

Type II error states that Probability of accepting null hypothesis given the fact that null hypothesis is false.

This is considered to be the most important error.

So, from the option given to us option C matches that failing to reject a false null hypothesis.

Answer:

0.2605, 0.2188, 1.33, 4, 1.0540, 1.4142

Step-by-step explanation:

A fair die is rolled 8 times.  

a. What is the probability that the die comes up 6 exactly twice?  

b. What is the probability that the die comes up an odd number exactly five times?  

c. Find the mean number of times a 6 comes up.  

d. Find the mean number of times an odd number comes up.  

e. Find the standard deviation of the number of times a 6 comes up.  

f. Find the standard deviation of the number of times an odd number comes up.

a. A die is rolled 8 times. If A represent the number of times a 6 comes up. For a fair die the probability that the die comes up 6 is 1/6 - Thus A ~ Bin(8, 1/6)

The probability mass function  of the random variable A is  

[tex]p(A) = \left \{ {\frac{8!}{x!(8 - x)!}*(\frac{1}{6} )^{A}*(\frac{5}{6} )^{8-A} } \right. for A=0,1, ...8[/tex]

hence, p(6 twice) implies P(A=2)

that is P(2) substitute A = 2

[tex]p(2) = \left \{ {\frac{8!}{2!(8 - 2)!}*(\frac{1}{6} )^{2}*(\frac{5}{6} )^{8-2} } \right. for A=0,1, ...8[/tex]

[tex]p(2)=\frac{8!}{2!6!} *(\frac{1}{6} )^{2} *(\frac{5}{6} )^{6}[/tex]  

p(2) = 0.2605  

b. If B represent the number of times an odd number comes up. For the fair die the probability that an odd number comes up is 0.5.

Thus B ~ Bin(8, 1/2 )

The probability mass function of the random variable B is given by

[tex]p(B) = \left \{ {\frac{8!}{B!(8 - B)!}*(\frac{1}{2} )^{B\\}*(\frac{1}{2} )^{8-B} } \right. for B=0,1, ...8[/tex]

hence p(odd comes up 5 times) is

[tex]p(x=5) = p(2)=\frac{8!}{5!3!} *(\frac{1}{2} )^{5} *(\frac{1}{2} )^{3}[/tex]

p(5) = 0.2188

c. let the mean no of times a 6 comes up be μₐ

   and let the total number of outcomes be n

   using the formula μₐ = nρₐ

   μₐ = 8 * 1/6

        = 1.33

d. let the mean nos of times an odd nos comes up be μₓ

   let the total outcomes be n = 8

   let the probability odd be pb = 1/2

   μₓ = npb

        = 8 * (1/2)

        = 4

e. the standard deviation of a random variable A is given as follows

σₐ [tex]= \sqrt{np(1-p)}[/tex]

where p = 1/6 (prob 6 outcome)

n = total outcomes = 8

  [tex]= \sqrt{8*\frac{1}{6}*\frac{5}{6} }[/tex]

  = 1.0540

f. the standard dev of the binomial random variable Y is given by

σ [tex]= \sqrt{np(1-p)}[/tex]

where p = 1/2 and n = 8

  =  [tex]\sqrt{8*\frac{1}{2} *\frac{1}{2} }[/tex]

  = 1.4142

Answer:

5.55% of broilers weigh between 1143 and 1242 grams

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 1511, \sigma = 198[/tex]

What proportion of broilers weigh between 1143 and 1242 grams?

This is the pvalue of Z when X = 1242 subtracted by the pvalue of Z when X = 1143.

X = 1242

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1242 - 1511}{198}[/tex]

[tex]Z = -1.36[/tex]

[tex]Z = -1.36[/tex] has a pvalue of 0.0869

X = 1143

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1143 - 1511}{198}[/tex]

[tex]Z = -1.36[/tex]

[tex]Z = -1.86[/tex] has a pvalue of 0.0314

0.0869 - 0.0314 = 0.0555

5.55% of broilers weigh between 1143 and 1242 grams

Answer:

(a) The value of P (X = 7) is 0.1388.

(b) The value of P (X ≥ 3) is 0.9380.

(c) The value of P (2 < X < 7) is 0.5433.

(d) [tex]\mu_{X}=6[/tex]

(e) [tex]\sigma_{X}=2.45[/tex]

Step-by-step explanation:

Let X = number of uranium fission tracks on per cm² surface area of the mineral.

The average number of track per cm² surface area is, λ = 6.

The random variable X follows a Poisson distribution with parameter λ = 6.

The probability mass function of a Poisson distribution is:

[tex]P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, 3...[/tex]

(a)

Compute the value of P (X = 7) as follows:

[tex]P(X=6)=\frac{e^{-6}(6)^{7}}{7!}=\frac{0.0025\times 279936}{5040}=0.1388[/tex]

Thus, the value of P (X = 7) is 0.1388.

(b)

Compute the value of P (X ≥ 3) as follows:

P (X ≥ 3) = 1 - P (X < 3)

              = 1 - P (X = 0) - P (X = 1) - P (X = 2)

              [tex]=1-\frac{e^{-6}(6)^{0}}{0!}-\frac{e^{-6}(6)^{1}}{1!}-\frac{e^{-6}(6)^{2}}{2!}\\=1-0.00248-0.01487-0.04462\\=0.93803\\\approx0.9380[/tex]

Thus, the value of P (X ≥ 3) is 0.9380.

(c)

Compute the value of P (2 < X < 7) as follows:

P (2 < X < 7) = P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6)

                   [tex]=\frac{e^{-6}(6)^{3}}{3!}+\frac{e^{-6}(6)^{4}}{4!}+\frac{e^{-6}(6)^{5}}{5!}+\frac{e^{-6}(6)^{6}}{6!}\\=0.08924+0.13385+0.16062+0.16062\\=0.54433\\\approx0.5443[/tex]

Thus, the value of P (2 < X < 7) is 0.5433.

(d)

The mean of the Poisson distribution is:

[tex]\mu_{X}=\lambda=6[/tex]

(e)

The standard deviation of the Poisson distribution is:

[tex]\sigma_{X}=\sqrt{\sigma^{2}_{X}}=\sqrt{\lambda}=\sqrt{6}=2.4495\approx2.45[/tex]

Answer:

(b) 15.50 to 16.50 ounces

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 16

Standard deviation = 0.25

Based on this information, between what two values could we expect 95% of all cans to weigh?

By the Empirical Rule, within 2 standard deviations of the mean. So

16 - 2*0.25 = 15.50 ounces

16 + 2*0.25 = 16.50 ounces

So the corret answer is:

(b) 15.50 to 16.50 ounces

Final answer:

By calculating two standard deviations from the mean in both directions, we determine that 95% of cans are expected to weigh between 15.5 and 16.5 ounces. Thus, option b is correct.

Explanation:

The question involves finding between which two values 95% of all cans of tomato soup would weigh, given that the mean weight is 16 ounces with a standard deviation of 0.25 ounces. This question can be answered by applying the empirical rule (also known as the 68-95-99.7 rule) for a normal distribution, which states that approximately 95% of the data falls within two standard deviations of the mean.

To calculate the range:

1. Subtract two standard deviations from the mean to find the lower limit.

16 ounces - (2 * 0.25 ounces) = 15.5 ounces

2. Add two standard deviations to the mean to find the upper limit.

16 ounces + (2 * 0.25 ounces) = 16.5 ounces

Therefore, we can expect 95% of all cans to weigh between 15.5 and 16.5 ounces, which corresponds to option (b) 15.50 to 16.50 ounces.

Answer:

P(X = 17) = 0.3002

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this problem we have that:

[tex]n = 18, p = 0.9[/tex]

We want P(X = 17). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 17) = C_{18,17}.(0.9)^{17}.(0.1)^{1} = 0.3002[/tex]

P(X = 17) = 0.3002

Answer:

P(X=17) = 0.3002 .

Step-by-step explanation:

We are given that the random variable X has a binomial distribution with the given probability of obtaining a success.

The above situation can be represented through Binomial distribution;

[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 18

            r = number of success = 17

           p = probability of success which in our question is given as 0.9 .

So, X ~ [tex]Binom(n=18,p=0.9)[/tex]

We have to find the probability of P(X = 17);

P(X = 17) = [tex]\binom{18}{17}0.9^{17} (1-0.9)^{18-17}[/tex]

               = [tex]18 \times 0.9^{17} \times 0.1^{1}[/tex]    { [tex]\because \binom{n}{r} = \frac{n!}{r! \times (n-r)!}[/tex] }

               = 0.3002

Therefore, P(X=17) = 0.3002 .

Answer:

(a) 4 possible outcomes

(b) Not possible, testing stops upon finding the bad battery,

Step-by-step explanation:

Let G denote a good battery and B denote a bad battery.

Whenever a bad battery is found, the batteries stop being tested.

(a) The outcomes for this experiment are:

B

GB

GGB

GGGB

There are 4 possible outcomes.

(b) The outcome GBGG is not possible since testing stops upon finding the bad battery, the outcome in this case would be GB.

Answer:16.5

Step-by-step explanation:

Answer:

11 7/10

Step-by-step explanation:

Lets make the fractions into common denominators, by mulitplying 4 by 5 and 5 by 4 (see below) and follow PEMDAS

3 1/4(5) +(3 1/4(5) + 5 1/5(4))

3 5/20+ (3 5/20+5 4/20)

Simplify like terms

3 5/20+ (8 9/20)

11 14/20

Simplify fraction

11 7/10

Answer:

Step-by-step explanation:

Hello!

X: nitrate concentration in the city's drinking water supply.

X~N(μ;δ²)

A concentration above 10 ppm is a health risk for infants less than 6 months old.

The reported nitrate concentration is between 1.59 and 2.52 ppm, values outside this range are considered unusual.

If any value of a normal distribution that is μ ± 2δ is considered unusual, it is determined that:

μ - 2δ= 1.59

μ + 2δ= 2.52

20) and 21)

I'll clear the values of the mean and the standard deviation using the given information:

a) μ - 2δ= 1.59 ⇒ μ = 1.59 + 2δ

b) μ + 2δ= 2.52 ⇒ Replace the value of Mu from "a" in "b" and clear the standard deviation:

(1.59 + 2δ) + 2δ= 2.52

1.59 + 4δ= 2.52

4δ= 2.52 - 1.59

δ= 0.93/4

δ= 0.2325

Then the value of the mean is μ = 1.59 + 2(0.2325)

μ = 1.59 + 0.465

μ = 2.055

22)

Acording to the empirical rule, 68% of a normal distribution is between μ±δ

Then you can expect 68% of the distribution between:

μ-δ= 2.055-0.2325= 1.8225

μ+δ= 2.055+0.2325= 2.2875

Correct option: C. 1.823 and 2.288 ppm

I hope it helps!

The probability that the sum of the dots on two dice will be 3 is 0.056, determined by finding the number of favorable outcomes (2) and dividing by the total number of outcomes (36).

The subject of this question is probability, specifically focusing on an experiment involving the tossing of two six-sided dice. To find the probability that the sum of the dots on the two top faces will be 3, we first need to determine the total number of possible outcomes when two dice are thrown. For one six-sided die, there are 6 possible outcomes. Therefore, when two dice are thrown, the total number of outcomes is 6 * 6 = 36.

Next, we need to find the number of outcomes where the sum of the dots would be 3. Looking at our dice, we can see that this can only happen in two ways: getting a 1 on the first die and a 2 on the second, or getting a 2 on the first die and a 1 on the second.

So, the number of favorable outcomes is 2.

Probability is defined as the number of favorable outcomes divided by the total number of outcomes. Hence, the probability of the sum of the dots being 3 when two dice are thrown is 2/36. To get this in three significant figures, we divide 2 by 36 which gives the decimal 0.0556. Therefore, the probability to three significant figures is 0.056.

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Answer:

No, there is not enough evidence at the 0.02 level to support the executive's claim.

Step-by-step explanation:

We are given that a publisher reports that 34% of their readers own a particular make of car. A random sample of 220 found that 30% of the readers owned a particular make of car.

And, a marketing executive wants to test the claim that the percentage is actually different from the reported percentage, i.e;

Null Hypothesis, [tex]H_0[/tex] : p = 0.34 {means that the percentage of readers who own a particular make of car is same as reported 34%}

Alternate Hypothesis, [tex]H_1[/tex] : p [tex]\neq[/tex] 0.34 {means that the percentage of readers who own a particular make of car is different from the reported 34%}

The test statistics we will use here is;

                T.S. = [tex]\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)

where, p = actual % of readers who own a particular make of car = 0.34

            [tex]\hat p[/tex] = percentage of readers who own a particular make of car in a

                  sample of 220 = 0.30

            n = sample size = 220

So, Test statistics = [tex]\frac{0.30 -0.34}{\sqrt{\frac{0.30(1- 0.30)}{220} } }[/tex]

                             = -1.30

Now, at 0.02 significance level, the z table gives critical value of -2.3263 to 2.3263. Since our test statistics lie in the range of critical values which means it doesn't lie in the rejection region, so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the actual percentage of readers who own a particular make of car is same as reported percentage and the executive's claim that it is different is not supported.

Answer:

750,0000

Step-by-step explanation:

Answer:

Yes, this a biased sampling method.

Step-by-step explanation:

The sampling done is a biased sampling method.

This is because usually people who are upset or dissatisfied with the service are the ones who write online reviews, as there are no other way to release their frustration with the service provided.

The bias is likely to be directed towards the proportion of people who are not satisfied with service.

Answer:

Step-by-step explanation:

Given that an urn contains five balls numbered 1 to 5

Two balls are drawn simultaneously.

a) X = the larger of two numbers drawn

Assuming balls are drawn without replacement, (since simultaneously drawn)

the sample space would be (1,2) (1,3)(1,4)(1,5) (2,3)(2,4)(2,5) (3,4) (3,5) (4,5)

n(S) = 10

n(x=2) = 1,

n(x=3) =2

n(x=4) = 3

n(x=5) = 4

Larger value  X can take values only as 2,3,4 or 5

X          2              3            4               5

p          0.1           0.2       0.3             0.4

-------------------------------------------

b) V = sum of numbers drawn

V can take values as 3, 4, 5, 6, 7, 8 or 9

V                  3        4             5          6           7             8          9

p                  0.1     0.1         0.2      0.2         0.2        0.1        0.1

The probability that the larger number drawn will be k follows a specific probability distribution, as does the sum of the two numbers drawn. Using the given information and principles of probability, we can determine the probabilities for each value of k for both X and V. For X, the probability distribution pX(k) is [1/5, 1/5, 3/10, 1/5, 1/5]. For V, the probability distribution pV(k) is [1/20, 1/10, 3/20, 1/10, 1/10, 1/10, 3/20, 1/10, 1/20].

(a) Let's consider each possible outcome to find pX(k), the probability that the larger number drawn will be k:

If k is 1, there is only one possible outcome: drawing (1, anything). The probability of this outcome is (1/5) * (4/4) = 1/5.

If k is 2, there are two possible outcomes: drawing (2, 1) or (2, 3). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) = 1/10 + 1/10 = 1/5.

If k is 3, there are three possible outcomes: drawing (3, 1), (3, 2), or (3, 4). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (2/4) = 1/10 + 1/10 + 1/10 = 3/10.

If k is 4, there are four possible outcomes: drawing (4, 1), (4, 2), (4, 3), or (4, 5). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (3/4) = 1/10 + 1/10 + 1/10 + 3/20 = 1/5.

If k is 5, there are five possible outcomes: drawing (5, 1), (5, 2), (5, 3), (5, 4), or (5, 5). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (4/4) = 1/10 + 1/10 + 1/10 + 1/10 + 1/5 = 1/5.

Therefore, the probability distribution pX(k) is:

pX(1) = 1/5

pX(2) = 1/5

pX(3) = 3/10

pX(4) = 1/5

pX(5) = 1/5

(b) Let's consider each possible outcome to find pV(k), the probability that the sum of the two numbers drawn will be k:

If k is 2, there is only one possible outcome: drawing (1, 1). The probability of this outcome is (1/5) * (1/4) = 1/20.

If k is 3, there are two possible outcomes: drawing (1, 2) or (2, 1). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 = 1/10.

If k is 4, there are three possible outcomes: drawing (1, 3), (2, 2), or (3, 1). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 + 1/20 = 3/20.

If k is 5, there are four possible outcomes: drawing (1, 4), (2, 3), (3, 2), or (4, 1). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 + 1/20 + 1/20 = 1/10.

If k is 6, there are five possible outcomes: drawing (1, 5), (2, 4), (3, 3), (4, 2), or (5, 1). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 + 1/20 + 1/20 + 1/20 = 1/10.

If k is 7, there are four possible outcomes: drawing (2, 5), (3, 4), (4, 3), or (5, 2). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 + 1/20 + 1/20 = 1/10.

If k is 8, there are three possible outcomes: drawing (3, 5), (4, 4), or (5, 3). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 + 1/20 = 3/20.

If k is 9, there are two possible outcomes: drawing (4, 5) or (5, 4). The probability of these outcomes is (1/5) * (1/4) + (1/5) * (1/4) = 1/20 + 1/20 = 1/10.

If k is 10, there is only one possible outcome: drawing (5, 5). The probability of this outcome is (1/5) * (1/4) = 1/20.

Therefore, the probability distribution pV(k) is:

pV(2) = 1/20

pV(3) = 1/10

pV(4) = 3/20

pV(5) = 1/10

pV(6) = 1/10

pV(7) = 1/10

pV(8) = 3/20

pV(9) = 1/10

pV(10) = 1/20

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Answer:

1) Number of scoops = 42

2)Number of scoops = 10

Step-by-step explanation:

Volume of the sink = (4000/3)π in³

1)

Diameter = 4 in      ∵   Radius = 4/2 = 2 in

Height = 8 in

Volume of the cylindrical cup =  [tex]\pi r^{2}h = \pi 2^{2} * 8 = 32\pi[/tex] in³

Number of cups of water that must be scooped out = Volume of the sink/ Volume of the cylindrical cup

= (4000/3)π / 32π    ==>  42

Number of scoops = 42

b)

Diameter = 8 in    ∵   Radius = 8/2 = 4 in

Height = 8 in

Volume of the cylindrical cup =  [tex]\pi r^{2}h = \pi 4^{2} * 8 = 128\pi[/tex] in³

Number of cups of water that must be scooped out = Volume of the sink/ Volume of the cylindrical cup

= (4000/3)π / 128π ==> 10

Number of scoops = 10

Answer:

Please find attached answer.

Step-by-step explanation:

The Naive Bayes model is likely to classify the document 'machine learning is fun' and 'christmas family fun' as 'entertainment', even when using Laplace smoothing.

The Naive Bayes model classifies texts based upon the likelihood of a particular term belonging to a given class. To find the target level for the document, you multiply the prior probability of the document being in a given class (either entertainment or education) with the likelihoods of the terms in the query document being in that class and you choose the class with the highest probability.

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Given that the equation of the line is [tex]y=4x-3[/tex]

We need to determine the point (2,7) lies on the line.

For a point to lie on the line, substituting the point in the equation of the line makes it valid.

Thus, substituting the point (2,7) in the equation of the line [tex]y=4x-3[/tex], we get;

[tex]7=4(2)-3[/tex]

[tex]7=8-3[/tex]

[tex]7\neq 5[/tex]

Thus, the both sides of the equation are not equal.

Substituting the point (2,7) in the equation makes the equation invalid.

Thus, the point (2,7) does not lie on the line  [tex]y=4x-3[/tex]

Answer:

75%

Step-by-step explanation:

Find the percentage corresponding to 42/56:  (0.75)(100%) = 75%

Answer:

75%

Step-by-step explanation:

Becauuuuuuseeee if you divide 42  by 56 it would be 0.75 and yeah. so take out the 0 and its 75%

Answer:

0.0241 or 2.41%

Step-by-step explanation:

Since each customer has a 17% probability of ordering decaffeinated coffee, the probability of a customer ordering a coffee with caffeine is:

[tex]P(C) = 1-0.17 = 0.83[/tex]

If customers make their decisions independently, the probability that all 20 order a coffee with caffeine is:

[tex]P(X=20)=P(C)^{20}\\P(X=20) = 0.83^{20}=0.0241=2.41\%[/tex]

The probability is 0.0241 or 2.41%.