Question

A normal distribution has a mean of 15 and a standard deviation of 5. If samples of size 25 are taken, and the sample means are calculated, describe the sampling distribution by answering the questions below:

What would the mean of the sampling distribution be?
What would the standard deviation of the sampling distribution be? Simplify your answer.

Answer 1

The mean of the sampling distribution when taking samples of size 25 from a normal distribution with a mean of 15 and a standard deviation of 5 would be 15. The standard deviation, or standard error, of the sampling distribution would be 1.

Step-by-step explanation:

For a normal distribution with a mean of 15 and a standard deviation of 5, when you take samples of size 25, the sampling distribution of the sample mean follows certain properties. According to the Central Limit Theorem, the mean of the sampling distribution would be equal to the population mean, which is 15. The standard deviation of the sampling distribution, often called the standard error, would be the population standard deviation divided by the square root of the sample size. Therefore, the standard error would be 5 / √25, which simplifies to 1.