Consider the following experiment: a soccer team in a tie-breaker has to take five shots on goal. The probability of making a goal is 0.75. You may assume that each shot is independent of the others; that is, making one shot does not affect the chances of making the next shot. Required:
a. If X is the random variable representing the number of goals scored, list all possible values of X.
b. What is the probability that the team makes all five shots, that is, makes five out of the five goals?
c. What is the probability that the team makes three or more shots?
d. What is the expected value of the variable "number of goals scored"?
e. Interpret the expected value: in this situation, what does it tell you?