Following a touchdown, a college football coach has the option to elect to attempt a two-point conversion; that is, two additional points are scored if the attempt is successful and none, if it is unsuccessful. The coach believes that the probability is 0.35 that his team will be successful in any attempt and that outcomes of different attempts are independent of each other. In a particular game the team scores 4 touchdowns and two-point conversion attempts were made each time.
a. What is the probability that at least 2 of these attempts will be successful?
b. Find the mean and standard deviation of the total number of points resulting from these 4 attempts.
c. What is the required success rate for completing one point conversions so that the same mean number of points are obtained?