In: Statistics and Probability
1. The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $100 and a standard deviation of $25. If the management wants to give free gifts to at most 2.5% of the customers, what should the amount be above which a customer would receive a free gift? Round your answer to the nearest two decimal places.
The Red Cross honors and recognizes its best volunteers from time to time. One of the Red Cross offices has received 10 nominations for the next group of 4 volunteers to be recognized. 5 of these 10 nominated volunteers are females. If the Red Cross office decides to randomly selected 4 names out of these 10 nominated volunteers, find the probability, rounded to four decimal places, that of these 4 volunteers exactly 1 is female.