The average height of an American male is 176. 9 centimeters with a standard deviation of 7. 62 centimeters. American male heights are normally distributed. Josie doesn't know about the metric system and only can deal with inches. She asks Siri how to convert from centimeters to inches and gets: One centimeter converts to about 0. 394 inches. Let X be the height in inches of a randomly selected American male,
a) Find the expected value of X.
b) Find the variance of X.
c) Find the standard deviation of X.
d) What is the 80th percentile of X?
e) What is the probability that X < 72?=””>
f) What is the probability that 65 < x=””>< 75=””>
g) If S is the sum in inches of the heights of 16 randomly selected American males, then what is the standard deviation of S?
h) If S is the sum in inches of the heights of 16 randomly selected American males, then what is the probability that S/16 is <>