You have decided to purchase a shirt for your mother for Christmas. You are aware that the upper arm length of American women over the age of 20 is roughly typical, with a mean of 34.5 centimeters (cm) and a standard deviation of 2.2 centimeters.

(a) How long should the upper arm of the shirt be to be large enough for a 95th percentile female?

(b) How long should the upper arm of the shirt be to be large enough for a 99th percentile male (consider the standard deviation of the upper arm for males is 2.5 cm, but you should calculate the upper arm mean value for male)?