Every year in early October Steven King buys pumpkins of one size from a farmer in Maine and then hires an artist to carve bewitching faces in them. He then tries to sell them at his produce stand in a public market in Boston.
The farmer charges Steven $2.50 per pumpkin and the artist is paid $2.00 per carved pumpkin. Steven sells a carved pumpkin for $8.00. Any pumpkins not sold by 5:00 p.m. on Halloween are donated to Steven's favorite children's hospital. Steven pays the artist $0.75 per pumpkin to rush the pumpkins to the hospital for the youngsters to enjoy.
Steven estimates the demand for his pumpkins this season to be uniformly distributed within a range of 30 to 70.
a. How many pumpkins should Steven have available for sale?
b. Based on your answer to (a), what is the probability that Steven will be short five or more pumpkins?