An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1 2 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 21 years of age. Using the minimum sample size with a 90% level of confidence, does it seem likely that the population mean could be within 8% of the sample mean? within 9% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table, Click here to view page 2 of the Standard Normal Table. (a) The minimum sample size required to construct a 90% confidence interval is students (Round up to the nearest whole number) (b) The 90% confidence interval is (. ) It does not seem likely that the population mean could be within 8% of the sample mean because the interval formed by the values 8% away from the sample mean overlaps but does not entirely contain the confidence interval It |does not seem likely that the population mean could be within 9% of the sample mean because the interval formed by the values 9% away from the sample mean |overlaps but does not entirely contain the confidence interval. (Round to two decimal places as needed )