Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that they're mean monthly income is $5747. How many standard deviation is the sample mean from the mean of the sample lien distribute distribution

Answers

Answer 1

The sample mean of $5747 is approximately 6.68 standard deviations below the mean of the sampling distribution.

To find out how many standard deviations the sample mean is from the mean of the sampling distribution, you can use the formula for z-score:

[tex]\[ z = \frac{{\text{{sample mean}} - \text{{population mean}}}}{{\text{{standard deviation of sampling distribution}}}} \][/tex]

In this case:

Sample mean [tex](\( \bar{x} \))[/tex] = $5747

Population mean[tex](\( \mu \))[/tex] = $5954

Standard deviation of sampling distribution [tex](\( \sigma_{\bar{x}} \)) = \( \frac{{\text{{population standard deviation}}}}{{\sqrt{\text{{sample size}}}}} \)[/tex]

Given the population standard deviation is $259 and the sample size is 70, you can calculate [tex]\( \sigma_{\bar{x}} \)[/tex]:

[tex]\[ \sigma_{\bar{x}} = \frac{{259}}{{\sqrt{70}}} \][/tex]

Let's calculate:

[tex]$\sigma_{\bar{x}}=\frac{259}{\sqrt{70}} \approx 30.94$[/tex]

Now, plug in the values:

[tex]$\begin{aligned} & z=\frac{5747-5954}{30.94} \\ & z \approx \frac{-207}{30.94} \approx-6.68\end{aligned}$[/tex]

So, the sample mean of $5747 is approximately 6.68 standard deviations below the mean of the sampling distribution.


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The social worker is responsible for helping clients .

Answers

"Social workers are responsible for helping individuals, families, and groups of people to cope with problems they're facing to improve their patients' lives." https://mswonlineprograms.org/job-duties-and-responsibilities-of-social-workers/

If you use this answer make sure to use quotation marks and include your source.

Answer:

The answer is: Restore their social functioning ability.

Explanation:

I had this question on my assignment, and I got it correct.  :)

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