A large corporation sponsors bowling leagues for its employees. The mean score for men was 154 pins with a standard deviation of 8 pins, while the women had mean score 131 pins and standard deviation 15 pins. The scores of men and women are thought to be independent. At the end of the season the league holds a tournament that randomly pairs men and women as opponents in the first round. Required:
1. If the distribution of differences in bowling scores is approximately normal, what is the probability that the man scores more points than the woman?

a. 0.888
b. 0.987
c. 0.912
d. 0.652

2. In statistics, an event is considered "unlikely" if the probability of it occurring is less than five percent. Based on your answer to part (a), would we consider the event of a man scoring more points than a woman a statistically "unlikely" event? Explain.

a. Yes, this is statistically unlikely, since the probability calculated in (C) is less than 5%.
b. Yes, this is statistically unlikely, since the probability calculated in (C) is greater than 5%.
c. No, this is NOT statistically unlikely, since the probability calculated in (C) is greater than 5%.
d. No, this is NOT statistically unlikely, since the probability calculated in (C) is less than 5%.