Graduate students applying for entrance to many universities must take a Miller AnalogiesTest. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100students applied for entrance into graduate school in physics.(a)[3] Find the mean and standard deviation of the sampling distribution of X.(b)[2] Find the probability that the average score of this group of students is higher than76.(c)[3] Find the probability that the sample mean deviates from the population mean by less than 2.(d)[4] Construct a 98% confidence interval for , the true mean test score.