A normally distributed population of scores has µ = 100 and s = 5. Based on this information, solve the following questions:
a. If a sample consisting of n=36 scores is selected from this population, what is the probability that the sample will have M=98 or greater?
b. If a sample consisting of n=4 scores is selected from this population, what is the probability that the sample will have M=98 or less?
c. If a sample consisting of n=25 scores is selected from this population, what is the probability that the sample will have M=102 or greater?
d. If a sample consisting of n=3 scores is selected from this population, what is the probability that the sample will have M=102 or less?
e. What happens to sm when n is increased and s is held constant? What does this finding suggest about using statistics to estimate parameters?