Question

A population has a mean of 75 and a standard deviation of 15. You randomly sample nine people from the population, and the mean of the nine people was 80. What is the z-score of your sample mean?

A. 1.0

B. 1.5

C. 2.0

D. 2.5

Answer 1

The z-score for a sample mean of 80, with a population mean of 75 and a standard deviation of 15, for a sample size of nine, is 1.0, which corresponds to option A.

Step-by-step explanation:

The z-score of the sample mean is a measure of how many standard deviations the sample mean is from the population mean. Since the population has a mean (μ) of 75 and a standard deviation (σ) of 15, and the sample mean (\( \bar{x} \)) is 80, we can use the formula:

Z = (\( \bar{x} \) - μ) / (σ/√n)

where n is the sample size. For this sample size of 9:

Z = (80 - 75) / (15/√9)

Z = 5 / (15/3)

Z = 5 / 5

Z = 1.0