Homework 26: The Normal Distribution

1. Section 5.6, #13.
2. Suppose that \(X\) is \(N_{-10,16}\) distributed. Find (a) \(P(X \gt -12)\), (b) \(P(-11 \lt X \lt -8)\).
3. Suppose that the height, in inches, of a 25 year old man is a normal random variable with paraters \(\mu=71\) and \(\sigma^2=6.25\). What percentage of 25 year old men are over 6 feet 2 inches tall? What percentage of men in the 6-footer club are over 6 foot 5 inches? How tall must a 25 year old man be in order to be in the top one percentile in height?
4. Everyone in a school is weighed. 40% weigh over 110 pounds and 13% weigh over 170 pounds. Assume that weight is normally distributed. Find the best choice for \(\mu\) and \(\sigma\).