The director of publications for a university is in charge of deciding how many programs to print for football games. Based on the data, the director has estimated the following probability distribution for the random variable X= number of programs sold at the university football game:

X25,00040,00055,00070,000

P(X)0.10.30.450.15

a.Compute the expected number of program sold at the university football game.

b.Compute the variance of program sold at the university football game.

c.Each program cost $1.25 to print and sells for $3.25. Any programs left unsold at the end of the game are discarded. The director has decided to print ether 55,000 or 70,000. Which of these two options maximizes the expected profit from program sale?