Intelligence Quotient (IQ) is a score obtained from a standardized test that is supposed to measure human intelligence. The scores on these tests are designed so the median is 100 points and a standard deviation is 15 points. (We will assume the mean is also 100 points.) 

a. If many, many random samples of 20 IQ scores are taken from the population, what are the mean and standard deviation of the resulting distribution of sample mean IQ scores? 

b. What sample size is needed so the standard deviation of the distribution of sample mean IQ scores is half that of a sample size of 20? 

c. What sample size is needed so the standard deviation of the distribution of sample mean IQ scores is one quarter that of a sample size of 20.