4 A hot dog vendor at Wrigley Field sells hot dogs for

$1.50 each. He buys them for $1.20 each. All the hot dogs he fails to sell at Wrigley Field during the afternoon can be sold that evening at Comiskey Park for $1 each. The daily demand for hot dogs at Wrigley Field is normally distributed with a mean of 40 and a standard deviation of 10.

a If the vendor buys hot dogs once a day, how many should he buy?

b If he buys 52 hot dogs, what is the probability that he will meet all of the day’s demand for hot dogs at Wrigley?