Question

The Emperor penguin, the largest of all penguins, has height (in inches) that follows a normal distribution with a mean of 40 and a standard deviation of 4. Which of the following would result in the most predictable sampling distribution of the sample mean. n = 9 n = 25 n = 4

Answer 1

Answer:

In this case, the most predictable sampling distribution of the sample mean is n=25.

Step-by-step explanation:

Every sample is expected to be around the mean, but it is expected to be more precise as the sample size becomes bigger.

The standard deviation of the sampling distribution is:

$s=\frac{\sigma}{\sqrt{n}}$

This means that bigger samples result in narrower distribution, therefore being more precise to estimate the mean.

In this case, the most predictable sampling distribution of the sample mean is n=25.