Questions: Question 3, 8.1.13 HW Score: 15%, 1.8 of Part 4 of 4 Points: 0 of 1 Complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph. Click the icon to view the graph. The value of μₓ̄ is 300 (b) What is the value of σₓ̄? The value of σₓ̄ is 20. (c) If the sample size is n=9, what is likely true about the shape of the population? A. The shape of the population is skewed left. B. The shape of the population is approximately normal. C. The shape of the population is skewed right. D. The shape of the population cannot be determined. (d) If the sample size is n=9, what is the standard deviation of the population from which the sample was drawn? The standard deviation of the population from which the sample was drawn is

Question 3, 8.1.13
HW Score: 15%, 1.8 of
Part 4 of 4
Points: 0 of 1

Complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph. Click the icon to view the graph.

The value of μₓ̄ is 300
(b) What is the value of σₓ̄?

The value of σₓ̄ is 20.
(c) If the sample size is n=9, what is likely true about the shape of the population?
A. The shape of the population is skewed left.
B. The shape of the population is approximately normal.
C. The shape of the population is skewed right.
D. The shape of the population cannot be determined.
(d) If the sample size is n=9, what is the standard deviation of the population from which the sample was drawn?

The standard deviation of the population from which the sample was drawn is

Transcript text: Question 3, 8.1.13 HW Score: 15%, 1.8 of Part 4 of 4 Points: 0 of 1 Complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph. Click the icon to view the graph. The value of $\mu_{\bar{x}}$ is 300 (b) What is the value of $\sigma_{\bar{x}}$? The value of $\sigma_{\bar{x}}$ is 20. (c) If the sample size is $\mathrm{n}=9$, what is likely true about the shape of the population? A. The shape of the population is skewed left. B. The shape of the population is approximately normal. C. The shape of the population is skewed right. D. The shape of the population cannot be determined. (d) If the sample size is $n=9$, what is the standard deviation of the population from which the sample was drawn? The standard deviation of the population from which the sample was drawn is

Solution

Solution Steps

Solution Approach

To solve the given questions, we need to follow these steps:

For part (a), the value of $\mu_{\bar{x}}$ is given as 300.
For part (b), the value of $\sigma_{\bar{x}}$ is given as 20.
For part (c), we need to determine the shape of the population based on the sample size $n=9$. Since the sample size is small, the shape of the population cannot be determined without additional information.
For part (d), we need to calculate the standard deviation of the population ($\sigma$) using the formula $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$.

Step 1: Given Values

We are provided with the following values:

The mean of the sampling distribution of the sample mean is given by $ \mu_{\bar{x}} = 300 $.
The standard deviation of the sampling distribution of the sample mean is given by $ \sigma_{\bar{x}} = 20 $.
The sample size is $ n = 9 $.

Step 2: Standard Deviation of the Population

To find the standard deviation of the population ($ \sigma $), we use the formula: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] Rearranging this gives: \[ \sigma = \sigma_{\bar{x}} \cdot \sqrt{n} \] Substituting the known values: \[ \sigma = 20 \cdot \sqrt{9} = 20 \cdot 3 = 60.0 \]

Step 3: Shape of the Population

Given that the sample size $ n = 9 $ is relatively small, we cannot definitively determine the shape of the population distribution without additional information. Therefore, we conclude that the shape of the population cannot be determined.