||(4)(a) The mean weight of a large group of people is 180 lb. and the standard deviation is 15 Ib. If the weights are normally distributed, find the probability that (1) a person picked randomly from the group will weigh between 160 Ib. and 180 lb. (11) the mean weight of four people taken randomly from the group will be between 160 lb. and 180 Ib. (b) A firm's record of past sales shows that 4 out of 10 customers who visited the store made purchases. Suppose on a very rainy morning 3 customers entered the store, (1) construct a probability distribution for the number that will make a purchase. (11) Find the expected value and the standard deviation for the probability distribution. (111) What's the probability that at least two of the customers will make purchases?