Final answer:
The probability that all 5 items will not be returned by the customer is 0.16807. The probability that more than one item will be returned by the customer is 0.89551. The mean number of items returned by the customer is 1.5.
Step-by-step explanation:
(a) To find the probability that all 5 items will not be returned by the customer, we can use the binomial probability formula. The probability of not returning a defective item is 1 - 0.3 = 0.7. So, the probability that all 5 items will not be returned is (0.7)^5 = 0.16807.
(b) To find the probability that more than one item will be returned by the customer, we can find the probability of 0 and 1 item being returned and subtract it from 1. The probability of 0 items being returned is (0.3)^5 = 0.00243. The probability of 1 item being returned is 5 * 0.3 * (0.7)^4 = 0.10206. So, the probability of more than one item being returned is 1 - 0.00243 - 0.10206 = 0.89551.
(c) The mean number of items returned by the customer can be calculated using the formula: mean = n * p, where n is the number of trials and p is the probability of success. Here, the number of trials is 5 and the probability of success is 0.3. So, the mean number of items returned by the customer is 5 * 0.3 = 1.5.