the standard deviation of the population for a given statistic is 37.4. a sampling distribution for the…

Explanation:

Step1: Recall the formula

The formula for the standard deviation of the sampling - distribution $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation, $\sigma_{\bar{x}}$ is the standard deviation of the sampling distribution, and $n$ is the sample size. We need to solve for $n$.

Step2: Rearrange the formula

From $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, we can get $n = (\frac{\sigma}{\sigma_{\bar{x}}})^2$.

Step3: Substitute the given values

We are given that $\sigma = 37.4$ and $\sigma_{\bar{x}}=5.29$. Substitute these values into the formula: $n=(\frac{37.4}{5.29})^2$.

Step4: Calculate the value of $n$

First, $\frac{37.4}{5.29}\approx7.07$. Then $n=(7.07)^2 = 49.9849$.

Step5: Round to the nearest whole number

Rounding $49.9849$ to the nearest whole number gives $n = 50$.

Answer:

50