An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages is normally distributed.

(a) Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.6 years. 

(b) The sample mean is 20 years of age. Using the minimum sample size with a 90% level of confidence, does it seem possible that the population mean could be within 7% of the sample mean? within 8% of the sample mean? Explain.