Question

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

Answer 1

Use z-scores:

z = (x - mean)/(sd/√n)
x = 115
mean = 100
sd = 15
n = 3

Once you have z, use a z-table to determine probability. If the probability is low, then it would be unusual for the mean of a sample of 3 to be 115 or more.

I hope this will help.

Answer 2

116