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 1.8 years. (b) The sample mean is 20 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 10% of the sample mean? within 11% 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 likely that the population mean could be within 10% of the sample mean because the interval formed by the values 10% away from the sample mean the confidence interval. It likely that the population mean could be within 11% of the sample mean because the interval formed by the values 11% away from the sample mean the confidence interval. (Round to two decimal places as needed.)