Exercise 101 of Chapter 2 referred to a multiple-choice exam in which 10 of the questions have two options, 13 have three options, 13 have four options, and the other 4 have five options. Let X = the number of questions a student gets right, assuming s/he is completely guessing.
a. Write a program to simulate X, and use your program to estimate the mean and standard deviation of X.
b. Estimate the probability a student will score at least one standard deviation above the mean.

Data From Exercise 101 Chapter 2

A 40-question multiple-choice exam is sometimes administered in lower-level statistics courses. The exam has a peculiar feature: 10 of the questions have two options, 13 have three options, 13 have four options, and the other 4 have five options. (FYI, this is completely real!) What is the probability that, purely by guessing, a student could get at least half of these questions correct? Write a simulation program to answer this question.