7. The Stanford-Binet IQ test has results that are normally distributed with a mean of 100. A principal in an elementary school believes that her students have above average intelligence and wants verification of her belief. She randomly selects 20 students and checks the student files. She finds the following IQ scores for these 20 students. IQ scores: 110,132, 98, 97, 115, 145, 77, 130, 114, 128, 89, 101, 92, 85, 112, 79, 139, 102, 103, 89 a. Compute the sample mean and sample standard deviation of the IQs of the students sampled. Round to 1 decimal place. (4 pts.) b. Construct a 95% confidence interval for the mean IQ of students at this school. Show all steps in the computation of the error and the interval endpoints. Round to 1 decimal place. (10 pts.) c. The confidence interval has a fairly large margin of error due to the small sample size. Suppose the principal wanted to estimate the mean IQ of her students with 95% confidence and with a margin of error of 1.5 points. Using the value of s from part (a), what sample size would be required? (8 pts.)