Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for baskets of tomatoes that is approximately normally distributed with a mean of 60 baskets of tomatoes and a standard deviation of 12 baskets of tomatoes.
a) If there are 75 baskets of tomatoes available to be sold at the roadside stand at the beginning of a day, what is the probability that they will all be sold by the end of the day?
b) Approximately how many baskets of tomatoes should the farmer have available to ensure that on average they meet 95% of the demand?