Question 1. The distribution of scores of students heading to college in the math section of the SAT follows a normal distribution with mean ,u = 520 and standard deviation 0' = 115. X = The score of a student heading to college in the math section of the SAT X = The mean score of 100 students heading to college in the math section of the SAT 2 X = The total score of 100 students heading to college in the math section of the SAT (Please show all formulas, calculations and the curves) [3) What math SAT score is 2 standard deviations below the mean? {b} What is the probability that the score ofa student is less than 480? {c} What is the distribution of X? [d] What is the probability that the mean scores of 100 students is between 518 and 530? {e} What is the distribution of E X? if} What is the probability that the total scores of 100 students is more than 51500? {g} What is the 65th percentile for the mean scores of 100 students? Question 2. A camp director is interested in the mean number of letters each child sends during his or her camp session. A survey of 25 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8. (Please show all formulas, calculations and the curve} [3) Find a 95% confidence interval for the mean number of letters each child sends during the camp session. Interpret this confidence intervals. {b} Suppose that the population standard deviation of 3 is given. If you wanted to estimate the mean number of letters each child sends during the camp session with 90% confidence, and a margin of error of 0.25, how large a sample would you need