Question

A simple random sample of 20 observations is derived from a normally distributed population with a known standard deviation of 3.2. You may find it useful to reference the z table.

a. Is the condition that X− is normally distributed satisfied?
Yes or No

Answer 1

The sampling distribution of the mean will be normally distributed as the sample is drawn from a normally distributed population and the sample size is sufficiently large.

Step-by-step explanation:

Yes, the condition that Þxe is normally distributed is satisfied. This is because the population from which the sample is drawn is normally distributed, and the sample size (n = 20) is sufficiently large for the Central Limit Theorem to apply.

Since we also know the population standard deviation (3.2), this means we can use the standard normal distribution, or z-test, for hypothesis testing.