A life satisfaction Test has a population mean of = 400 and a population standard deviation of =120. Suppose you randomly select a sample of 100 participants and administer the Life Satisfaction Test to each participant.

a. What would you expect the mean of this sample to be?

b. What is the standard error of the mean for samples of size 100 from this population

c. What is the probability that this sample will be one of the samples that will have a mean Life Satisfaction score between 390 and 410? P(390 < x < 410) =?