Chapter 8.5, Problem 12E

The time between infection and the display of symptoms for streptococcal sore throat is a random variable whose probabililty density function can be approximated by $f\left(x\right)=\frac{1}{15,676}{t}^2{e}^{-0.05t}\text{ if }0\le t\le 150$ and $f\left(t\right)=0$ otherwise (t measured in hours).

(a) What is the probability that an infected patient will display symptoms within the first 48 hours?

(b) What is the probability that an infected patient will not display symptoms until after 36 hours?