A sample of n = 16 scores is obtained from a population with a mean of 70 and standard deviation of 20. If the sample mean is 75, then the z-score corresponding to the sample mean is ____.

Question

A sample of n = 16 scores is obtained from a population with a mean of 70 and standard deviation of 20. If the sample mean is 75, then the z-score corresponding to the sample mean is ____. Hint: You need to use the sampling distribution of the mean for a sample size of 16 and population standard deviation of 20.

Answer 1

75-70 = 5

5/20 = 1/4 = 25/100 = .25 = z score

75 is 0.25 standard deviations above the mean

take the difference from the mean and divide by the standard deviation to get the z score