In baseball, a "no-hitter" is a regulation 9-inning game in which the pitcher yields no hits to the opposing batters. Chance (Summer 1994) reported on a study of no-hitters in Major League Baseball (MLB). The initial analysis focused on the total number of hits yielded per game per team for all 9-inning MLB games played between 1989 and 1993. The distribution of hits/9-innings is approximately normal with mean 8.72 and standard deviation 1.10.
a. What percentage of 9-inning MLB games results in fewer than 6 hits?
b. Demonstrate, statistically, why a no-hitter is considered an extremely rare occurrence in MLB.