31. A concert has three pieces of music to be played before intermission. The time taken to play each piece has a normal distribution. Assume that the three times are independent of one another. The mean times are 15, 30, and 20 minutes, respectively, and the standard deviations are 1, 2, and 1.5 minutes, respectively. What is the probability that this part of the concert takes at most one hour? Are there reasons to question the independence assumption?

Explain.