An office supply company conducted a survey before marketing a new paper shredder designed for home use. In this survey, 80% of the people who used the shredder were satisfied with it. Because of this high acceptance rate, the company decided to market the new shredder. Assume that 80% of all people who will use it will be satisfied. On a certain day, seven customers bought this shredder.

a. Let X denote the number of customers in this sample of seven who will be satisfied with this shredder. Find the mean and standard deviation of X.

b. Find the following probabilities:

i. that exactly four of the seven customers will be satisfied.

ii. that at most three of the seven customers will be satisfied.

iii. that at least four of the seven customers will be satisfied.

iv. that between one and three (inclusive) of the seven customers will be satisfied.

v. that at least five of the seven customers will not be satisfied.