Question

A sample is taken from a normal distribution with μ=105 and σ=25, where n=25. Calculate the standard error of the mean (SEM) for this sample.

a) 5
b) 10
c) 25
d) 5/√25

Answer 1

The standard error of the mean (SEM) for a sample size of 25, taken from a normal distribution with a population standard deviation of 25, is calculated to be 5.

Step-by-step explanation:

The student has given a scenario where a sample is taken from a normal distribution with a mean (μ) of 105 and a standard deviation (σ) of 25, and the sample size (n) is 25. To calculate the standard error of the mean (SEM) for this sample, you use the formula SEM = σ / √n, where σ is the population standard deviation and n is the sample size. Substituting the given values in the formula, SEM = 25 / √25 = 25 / 5 = 5. Therefore, the standard error of the mean for this sample is 5.