Chapter 18, Problem 27E

(a)

To determine

To find out what is the sampling distribution model for the sample mean and describe the shape, center and spread.

Answer to Problem 27E

The sampling distribution model for the sample mean is normal.

Explanation of Solution

It is given in the question that a sample is chosen randomly from a population that can be described by a Normal model. As, we know that the sample is randomly selected and also the population is described by the normal model. Therefore we can say that the sampling distribution model for the sample mean is normal distribution. And the shape of the model will be symmetric, the center of the model will be at $\mu$ and the standard deviation will be $\frac{\sigma }{\sqrt{n}}$ .

(b)

To determine

To explain what is the effect on this sampling distribution model if we choose a larger sample.

Answer to Problem 27E

It will not affect the mean but the standard deviation will decrease.

Explanation of Solution

It is given in the question that a sample is chosen randomly from a population that can be described by a Normal model. Thus, if we choose a larger sample then increasing the sample size will not change the mean but will make the standard deviation smaller because doing so decreases variability.