1. Assume that the length of a typical televised baseball game including all the commercial timeouts follows a Normal distribution with a mean of 2.5 hours and a standard deviation of 0.37 hours. Now consider a televised baseball game that begins at 2 p.m.
a. If the next regularly scheduled broadcast program is at 5.00 p.m., what is the probability that the baseball game will cut into that program?
b. If the game is over before 4.30 p.m., another half-hour show can be inserted between 4.30 and 5.00 p.m. What is the probability of this occurring?
c. If the game is over before 4.00 p.m., an hour-long show can be inserted between 4.00 and 5.00 p.m. What is the probability of this occurring?
d. Can you provide a cut-off time by which you can be 99% sure that the baseball game would end?
e. Can you provide lower and upper cut-offs times such that the probability of the game ending between these times is 95%?