Please show all work, I want to understand how to attack and complete the problem.

QMB3200 - Exam#1

1. A Poll showed that 25% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 15 Americans is selected as part of a study of the state of the nation.
   1. a) Compute the probability that exactly 5 of the 15 Americans surveyed are satisfied with the way things are going in the United States.
   2. b) Compute the probability that at least 3 of the Americans surveyed are satisfied with the way things are going in the United States.
   3. c) Compute the probability that no more than 4 of the Americans surveyed are satisfied with the way things are going in the United States.
   4. d) Compute the probability that more than 2 but less than 6 of the Americans surveyed are satisfied with the way things are going in the United States.
   5. e) Compute the expected value, variance, and standard deviation of the number of Americans who are satisfied with the way things are going in the United States.