The time between infection and the display of symptoms for streptococcal sore throat is a random variable whose probability density function can be approximated by f(t) = 1/15,676 t²e^–0.05t if 0 ≤ t ≤ 150 and f(t) = 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?