If np >5 and nq>5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial distribution if np <5 or nq< then state that the normal approximation is not suitable.
To estimate the probability of getting fewer than 4 successes in a binomial distribution, we can use the normal distribution as an approximation based on the conditions np > 5 and nq > 5. By calculating the mean and standard deviation of the normal distribution, we can use a z-score to find the estimated probability. In this case, the estimated probability is approximately 0.1709.
Explanation:The given question requires us to estimate the probability of getting fewer than 4 successes in a binomial distribution. To determine if we can use the normal distribution as an approximation, we need to check if both np and nq are greater than 5. In this case, np = 13 * 0.4 = 5.2 and nq = 13 * 0.6 = 7.8, so both conditions are satisfied. Thus, we can use the normal distribution as an approximation. Let's estimate P(fewer than 4) using the normal distribution.
The mean of the normal distribution is given by μ = np = 13 * 0.4 = 5.2. The standard deviation is calculated using the formula σ = √(npq), where q = 1 - p. So, q = 1 - 0.4 = 0.6. Plugging in the values, we get σ ≈ √(13 * 0.4 * 0.6) ≈ 1.789. Now, we can use the normal distribution to estimate the probability.
Using the z-score formula z = (x - μ) / σ, where x is the number of successes we want to estimate the probability for, we can find the z-score for 3.5 (less than 4). z = (3.5 - 5.2) / 1.789 ≈ -0.951. Now, we can use a standard normal distribution table or calculator to find the cumulative probability for this z-score. P(fewer than 4) = P(z < -0.951) ≈ 0.1709 (approximately). Therefore, the estimated probability of getting fewer than 4 successes in the given binomial distribution is approximately 0.1709.
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Firstly, we would have to evaluate whether a normal approximation would be useful to use. However, given our conditions where `n` is 13, `p` is 0.4, `q` (the complement of `p`) is 1 - 0.4 or 0.6, we can clearly use the normal approximation to the binomial distribution because both `np` (13 * 0.4 = 5.2) and `nq` (13 * 0.6 = 7.8) are greater than 5.
For the normal approximation, we begin by calculating the mean (µ) and standard deviation (σ) of the binomial distribution. The mean of a binomial distribution is calculated as `np` hence in our case, `np` is 13 * 0.4 which is equal to 5.2. To find the standard deviation, we use the formula `sqrt(npq)`, so in our case, we have`sqrt(13 * 0.4 * 0.6)`, which is approximately 1.76635.
Now, to find the probability of getting fewer than 4, we would calculate a z-score for the value of x = 4. This helps convert the raw scores in a dataset into a standardised form, allowing us to better understand the position of individual scores in relation to the rest of the dataset. The z-score is calculated as `z = (x - µ) / σ` . With x being 4, µ is 5.2, and σ is 1.76635, our z-score will be (4 - 5.2) / 1.76635, which gives us approximately -0.67937.
Now, the last step is to find the cumulative probability associated with this z-score. In essence, the cumulative probability associated with a z-score tells you the probability that a certain observation will occur given a standard normal distribution (which is our case, as we've standardised our dataset using the z-score). Checking a z-table, or by using the cumulative distribution function for a value of z = -0.67937, the associated probability is approximately 0.24845.
So the final probability that we will get fewer than 4 is approximately 0.24845 or 24.85% when we use the normal distribution as an approximation to the binomial distribution.
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How do you prove that ABE is congruent to DBC?
Which expression is a cube root of 2?
A) Cube root of 2 (cos (120 degrees) + i sin (120 degrees))
B) Cube root of 2 (cos (40 degrees) + i sin (40 degrees))
C) Cube root of 2 (cos (280 degrees) + i sin (280 degrees)) ...?
Answer with explanation:
[tex]z=2^{\frac{1}{3}}\\\\z^3=2\\\\z^3=2 \times (1 + 0 i)\\\\z^3=2 \times [\cos 0^{\circ} + i \sin 0^{\circ}]\\\\z^3=2 \times [\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})],where,k=0,1,2,\\\\z=[2\times[ (\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})]]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}\times[\cos \frac{2 k\pi+ 0^{\circ}}{3} + i \sin\frac{(2 k\pi+0^{\circ})}{3}]\\\\Z_{0}=2^{\frac{1}{3}},for, k=0\\\\z_{1}=2^{\frac{1}{3}}\times[\cos \frac{(2\pi)}{3} + i \sin\frac{(2\pi)}{3}][/tex]
[tex]z_{1}=2^{\frac{1}{3}}\times[\cos(120^{\circ})+i\sin(120^{\circ})],\text{Used Demoiver's theorem}[\cos A + i\sin A]^k=\cos Ak + i\sin Ak[/tex]
Option A: →Cube root of 2 [cos (120 degrees) + i sin (120 degrees)]
HELP ASAP!!!
The best-selling book Samantha has been waiting for hit the shelves at $21.56. What percent discount was this off the cover price of $26.95?
A. 20%
B. 25%
C. 30%
D. 35%
Which of the following describes the positive solution to the equation below? The solution is greater than one but less than two. The solution is greater than zero but less than one. The solution is an irrational number. The solution is greater than two but less than three. The solution is a rational number. The solution is a repeating decimal.
The positive solution to the equation is a rational number between one and two.
Explanation:The positive solution to the equation is a rational number. It is greater than one but less than two. To find the solution, we would need to see the equation itself. However, based on the given options, the only option that fits the criteria of being between one and two and being a rational number is 'The solution is greater than one but less than two.'
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Show problem 737÷2 worked out for the answer
Round 63.3 to the nearest tenth
You have $270 in your bank account. You plan to save $80 from your paycheck each week. Which graph shows your bank account balance at the end of each week?
Answer: The below graph shows the given situation.
Step-by-step explanation:
Let x represents the number of week, and y represents the total balance in the account after x weeks.
Since, initially the amount in the account = $ 270
According to the question,
Every week $80 is saved.
Thus, the total saving in x weeks = 80 × x = 80x
Since the total amount in x weeks = Initial amount + total saving.
⇒ y = 80x + 270
Which is the equation of line that shows the given situation.
x-intercept of the line is (-27/8,0)
y-intercept = (0,270)
If x=1 y = 350
If x=2 y= 430
If x=3 y =510
Thus, the points of the line are (1,350), (2,430), (3,510)
Hence we can draw the graph with help of above information.
What is the factorization of the trinomial below?
x2 - 10x + 25
A. (x - 25)(x + 1)
B. (x - 25)(x - 1)
C. (x - 5)(x - 5)
D. (x - 5)(x + 5)
ending balance 1 59.75 outstanding deposits 175 .46 outstanding checks 231 .69 what is the balance
To calculate the balance, add the outstanding deposits to the ending balance and subtract the outstanding checks.
Explanation:To calculate the balance, we need to start with the ending balance and make adjustments for outstanding deposits and outstanding checks. First, add the outstanding deposits to the ending balance: 59.75 + 175.46 = 235.21. Next, subtract the outstanding checks from the previous result: 235.21 - 231.69 = 3.52. Therefore, the balance is $3.52.
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72/60 in simplest form
Hakeem's frog made three quick jumps. The first was 1 meter. The second jump was 85 centimeters. The third jump was 400 millimeters. What was the total length in centimeters of the frog's three jumps?
Answer: 225 Centimeters
Step-by-step explanation:
What is the rational number equivalent to
Isabella paid one of her bill late and owed a 4% late fee was 780. How much was Isabella's original bill in dollar
The original bill amount that Isabella owed before the late fee was $19,500.
We need to understand the relationship between the late fee and the original bill amount.
Isabella was charged a late fee of 4% of the original bill amount, and this late fee was $780.
Let's use the variable x to represent the original bill amount. Since the late fee is 4% of the original bill, we can write the equation:
[tex]0.04x = 780[/tex]
To find x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.04:
[tex]x = \frac{780}{0.04}[/tex]
Now, we can calculate this value:
[tex]x = 19500[/tex]
integrate 1/((x^5)*sqrt(9*x^2-1)) ...?
1/5 (7-3b) > 2
which of the following gives all values of b that satisfy the inequality above?
A) b< -1
B) b> -1
C) b< 1
D) b> 1
The value of b that satisfy the inequality are; B) b> -1 and C) b< 1
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
We have given an inequality;
1/5 (7-3b) > 2
To solve for b;
(7-3b) = 10
-3b = 10 - 7
-3b = 3
b = -3/3
b = -1
Thus, the value of b that satisfy the inequality are; B) b> -1 and C) b< 1
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The correct solution for the given inequality 1/5 (7-3b) > 2 gives us b < -1. Option A is correct.
The given inequality is 1/5 (7-3b) > 2. To find the range of values for b that satisfy this inequality, follow these steps:
Multiply both sides of the inequality by 5 to eliminate the fraction: 7 - 3b > 10.
Subtract 7 from both sides of the inequality: -3b > 3.
Since we are dividing by a negative number, remember to reverse the inequality sign: b < -1.
Therefore, the correct answer is b < -1, which is option A.
How many solutions are there to the equation below?
13x + 195 = 13(x + 15)
A. 0
B. 1
C. infinitely many
1. Determine whether each coefficient is positive or negative
2. Choose the coefficient closest to 0
3. Choose the coefficient with the greatest value
Graph A & C are negative
Graph B & D are positive
The coefficient closest to 0 is B
The coefficient with the least value is A
Hope this helped :3
slope of j (0,0) , k (-2,8)
The slope of the line passing through points J (0,0) and K (-2,8) is calculated using the slope formula and results in a slope of -4.
The question asks to calculate the slope of the line passing through points J (0,0) and K (-2,8). The slope of a line is found by the formula
slope = (y'' - y') / (x'' - x'), where (x', y') and (x'', y'') are the coordinates of two distinct points on the line. Substituting the given points into this formula gives us
slope = (8 - 0) / (-2 - 0) = 8 / -2 = -4.
What is the approximate value of x in the diagram below? (Hint: You will need to use one of the trigonometric ratios given in the table.
"
The approximate value of 'x' in the diagram is 31. 64
How to determine the value of xUsing the formula, tan α = opposite side/ adjacent side
Opposite side = side opposite the angle
Adjacent = the other side
IF α = 36°
Opposite = 23
Adjacent = x
tan 36 = 0. 727
Substitute values into the formula
tan 36° = 23/ x
0.727 = 23/ x
Make 'x' subject by cross multiplying
x * 0. 727 = 23
x = 23/ 0. 727
x = 31. 64
Thus, the approximate value of 'x' in the diagram is 31. 64
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. Each U.S. coin is mapped to its monetary value. Tell whether this situation represents a function. Explain your reasoning. If the situation represents a function, give the domain and range.
Two shopping carts are pushed with the same force. One cart has a larger mass than the other. How does the mass of the shopping carts affect their acceleration?
The cart with the smaller mass will accelerate faster.
The cart with the larger mass will accelerate faster.
The cart with the smaller mass will not accelerate as fast as that with the larger mass.
Both shopping carts will accelerate at the same rate since they are the same size.
what is 1/4% in dollars of 3 million dollars
Choose the right answer.
Two hundred fifty tickets are sold at a fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is
6%
7.5%
15%
Answer:
Option A. 6%
Step-by-step explanation:
250 tickets are sold at a fund raiser.
Sarah buys 15 tickets.
The probability that she will win the prize quilt = [tex]\frac{15}{250}[/tex]
= 0.06 = 6%
The probability that Sarah will win is 6%.
Which rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I'?
(x, y)→(x - 8, y - 7)
(x, y)→(x - 7, x - 8)
(x, y)→(x - 4, x - 5)
(x, y)→(x - 5, y - 4)
5417 times 2.4 equals what
Factor completely: 2a2 − a − 10
Prime
(2a + 5)(a − 2)
(2a − 2)(a + 5)
(2a − 5)(a + 2) ...?
Answer:
(2a − 5)(a + 2)
Step-by-step explanation:
Evaluate -10 × X × 5 when X= -1
The expression -10 × X × 5 when X = -1 is equal to 50.
Evaluating the expression -10 × X × 5 when X= -1To evaluate -10 × X × 5 when X = -1, we substitute -1 for X in the expression:
-10 × (-1) × 5
Following the order of operations, we first perform the multiplication:
-10 × (-1) × 5 = 10 × 5
-10 × (-1) × 5 = 50
using the above as a guide, we have the following:
-10 × X × 5 when X = -1 is equal to 50.
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The revenue from selling x shirts is r(x) = 12x.
The cost of buying x shirts is c(x) = 5x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 7x – 20
B. p(x) = 17x + 20
C. p(x) = 17x – 20
D. p(x) = 7x + 20
Answer:
p(X)=7x-20
Step-by-step explanation:
correct answer
What is difference between a tilt level and a dumpy level?
A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. The main difference is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.
Explanation:A tilt level and a dumpy level are both surveying instruments used for measuring horizontal distances and vertical elevations. However, there are some key differences between the two.
Tilt Level: A tilt level, also known as a tilting level, is a type of level that utilizes a compensator mechanism to maintain a level plane even when the instrument itself is not level. This compensator allows for accurate measurements and eliminates the need for manually leveling the instrument each time.
Dumpy Level: A dumpy level, on the other hand, is a more traditional type of level that requires manual leveling before each use. It consists of a telescope mounted on a tripod, and the instrument is adjusted using leveling screws to ensure that it is perfectly horizontal. The dumpy level does not have a compensator like the tilt level, so the instrument needs to be leveled manually to obtain accurate measurements.
In summary, the main difference between a tilt level and a dumpy level is that the tilt level has a built-in compensator that eliminates the need for manual leveling, while the dumpy level requires manual leveling before each use.