The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function shown below. Find the probability that a bottle of this medicine will have a shelf life of (a) at least 150 days; (b) anywhere from 20 to 80 days. 5,000 3 X>0 f(x) (x+ 50) %D 0, elsewhere (a) The probability of a shelf life of at leas (Type an integer or decimal rounded to three decimal places as needed.) days is