I need proper solution for each part and with full explanation Neat and clean please

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 65th percentile for the mean scores of 100 students