Exercise 2: The Normal Distribution.

The function NORMDIST(x, mu, sigma, TRUE) computes the probability that a normal observation with a fixed mean (mu) and standard deviation (sigma) is less than x. There is also a function for computing the inverse operation: the function NORMINV(p, mu, sigma) computes a value x such that the probability that a normal observation is less than x is equal to P.

A. Compute the probability that an observation from a N(3, 5) population is less than 7.

B. Find the number x such that P{ N(4, 4) < x } = .75, i.e., such that a normal observation with mean 4 and standard deviation 4 has probability .75 of being less than x.

C. If the heights of 17-year-old girls are known to be normally distributed with mean 64 inches and standard deviation 3 inches, how tall must Taylor be when she is 17 so that she will be taller than 73% of other girls her age?