Public Policy and Political Science The President of the United States gives a State of the Union Address every year in late January or early February. Since Lyndon Johnson's address in 1966, Richard Nixon gave some of the shortest messages, and Bill Clinton presented a 1-hour and 28-minute address in 2000. The mean length for these addresses is 51.75 minutes and the standard deviation is 14.37 minutes. Assume the length of a State of the Union Address is normally distributed.

a. What is the probability that the next State of the Union Address will be between 45 and 55 minutes long?

b. What is the probability that the next State of the Union Address will be more than 90 minutes long?

c. What is the probability that the next two State of the Union Addresses will be less than 30 minutes long?