Question: The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 86 and a standard deviation of 11. A sample of 50 students is selected at random from the entire freshman class. Based on this information, what is the standard deviation of the sampling distribution of the sample mean?

(a) Referring to problem 1_3.4, what is the probability that the sample mean differs from the population mean by less than 3?

(b) Referring to problem 1_3.4, within what limits would you expect the sampling average to be with a probability of .90 or 90%?