Question

question #9 given a standard deviation of σ = 35 and a sample size of n = 85, calculate the standard deviation of the sampling distribution. 0.412 3.796 14368 2.429 question #10 for a population, the mean is 24,050 mm with a standard deviation of 7,238 mm. determine the mean and standard deviation of a sampling distribution of size n = 30 pulled from this population. mean: 24,050 mm standard deviation: 1,321 mm mean: 24,050 mm standard deviation: 7,238 mm mean: 4,391 mm standard deviation: 1,321 mm mean: 4,391 mm standard deviation: 7,238 mm

Explanation:

Step1: Recall the formula for standard deviation of sampling distribution

The formula for the standard deviation of the sampling distribution (also known as the standard error) is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step2: Solve Question #9

Given $\sigma = 35$ and $n = 85$.
$\sigma_{\bar{x}}=\frac{35}{\sqrt{85}}$
$\sqrt{85}\approx9.22$
$\sigma_{\bar{x}}=\frac{35}{9.22}\approx3.796$

Step3: Solve Question #10

The mean of the sampling distribution $\mu_{\bar{x}}$ is equal to the population mean $\mu$. So, $\mu_{\bar{x}} = 24050$ mm.
The standard deviation of the sampling distribution $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma = 7238$ mm and $n = 30$.
$\sqrt{30}\approx5.48$
$\sigma_{\bar{x}}=\frac{7238}{5.48}\approx1321$ mm

Answer:

Question #9: B. 3.796
Question #10: A. Mean: 24,050 mm, Standard Deviation: 1,321 mm