Let Z be a normally distributed random variable with mean 100 and standard deviation 15.

a. What is the probability that Z is between 90 and 100? -> 0.2475

Transform the uniform variates from above into normal variates with mean 10 and standard deviation 5, using the inverse cumulative distribution function (CDF) for the normal distribution.

1. What is the maximum value in your new normal sample?

2. What is the p-value of a Kolmogorov-Smirnov test of this new sample against the theoretical normal distribution it simulates?