Question: The ages of an airline’s aircraft are normally distributed with mean 7.5 years and standard deviation 2.5 years. Supposedenotes the age of one of the aircraft in this airline’s fleet. Find the following probabilities.

a) \(\Pr \left( 5.625\le X\le 12.625 \right)\)

b) \(\Pr \left( X\ge 3.125 \right)\)

c) \(\Pr \left( X\le 11.25 \right)\)

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?