In the population, "intelligence quotient" scores (IQ's) are approximately normally distributed with a mean of 100 and a standard deviation of 15.Suppose we plan to obtain IQ scores of a random sample of n = 30 individuals, and then we'll compute the sample mean and sample standard deviation.

Suppose you were unsure of the value of the population standard deviation, and so you plan to use only the sample standard deviation.Find theexact probabilitythat the sample mean will be within one-third of onesamplestandard deviation of the population mean.