3. Hospitalization length. The average length of a hospital stay in the US is 9 days with standard deviation of 3 days. Assume a simple random sample of 100 patients is obtained and the mean stay for 100 patients is obtained. What is the probability that the average length of stay for this group of patients will be less than 9.6 days? To answer this question, we usually think of the following steps: (a) What is the mean of the sampling distribution of 2 for samples of size 100. (b) What is the standard deviation of the sampling distribution of 2 for samples of size 100. (c) What is the probability to obtain a sample mean less than 9.6 days? 4. ACT scores. The scores of students on the ACT college entrance examination in a recent year had a Normal distribution. with mean = 18.6 and a standard deviation of σ = 5.9. (a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher? (b) Now take a simple random sample of 50 students who took the test. What are the mean and standard deviation of the sample mean score 2 of these 50 students? (c) What is the probability that the mean score of these students is 21 or higher?