Question 1. The distribution of scores of students heading to college in the math section of the SAT follows a normal distribution with mean / = 520 and standard deviation o = 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 EX = The total score of 100 students heading to college in the math section of the SAT (Please show all formulas, calculations and the curves) (a) What math SAT score is 2 standard deviations below the mean? (b) What is the probability that the score of a 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? (f) What is the probability that the total scores of 100 students is more than 51500? (g) What is the 65" 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) (a) 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