a normal population has a mean 100 and variance 25. how large must the sample size be if we want the standard error of the sample average to be at most 1.5

A sample size of 12 is needed.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation(square root of the variance) , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation, which is also called standard error, .

In this question:

How large must the sample size be if we want the standard error of the sample average to be at most 1.5

We need n for which s = 1.5.

Rounding up

A sample size of 12 is needed.