Question: The ages of an airline’s aircraft are normally distributed with mean 8.5 years and standard deviation 2.5 years. Suppose \[X\] denotes the age of one of the aircraft in this airline’s fleet. Find the following probabilities.

a) \[P\left( 5.75\le X\le 13.0 \right)\]

b) \[P(X\ge 4.75)\]

c) \[P\left( X\le 11.25 \right)\]

d) The airline considers an airplane old if its age is in the top 5% of the fleet. How old must, at minimum, a plane be to be considered old.

e) The airline considers an airplane new if its age is in the bottom 5% of the fleet. What is the maximum age of a new airplane?