Larry is a 63% free-throw shooter, that is to say that anytime Larry attempts a free-throw, there is a 63% chance he will make it.

Larry will attempt 80 free throws. Assume each attempt is independent of every other attempt. Let X be the number of free throws Larry makes out of 80 and let Pbe the proportion of the 80 attempts Larry makes.

a) What is the mean of X?

b) What was the standard deviation of X?

c) What is the mean of P?

d) What was the standard deviation of P?

e) Using the normal curve, approximate the probability that Larry makes over half of the 80 free throws.  In other words we seek either P( X> 40 ) or equivalently P( P> 0.5 ).