A university administrator is studying the distribution of ACT scores (with possible scores between 1-36) for new rst-year students at their university. Let Y denote the ACT score of one such student. The researcher models student ACT scores as following a normal distribution (i.e.,the population distribution is normal) and randomly samples n = 16 students from the population of rst-year students. The sample mean is g and the sample standard deviation is s. Answer the following questions. (If the exact values you need to solve these problems are not available in the appropriate table, use the closest values that are available.) (a) Assume that the population mean of the efciencies is ,u = 21 but that the population stan- dard deviation is unknown. The calculated sample standard deviation is s = 4. What is the probability that the sample mean is within 2 points of the population mean? (6 pts) (b) Find the sample size required to ensure that the sample mean ACT score is within 1 point of the population mean score with probability 0.90. Assume that the population standard deviation is a = 4. (6 pts)