Most Major League baseball parks have a device to measure the speed of every pitch. The results are often displayed on a scoreboard and tracked by coaches. A random sample of pitches made during the...

Most Major League baseball parks have a device to measure the speed of every pitch. The results are often displayed on a scoreboard and tracked by coaches. A random sample of pitches made during the first inning of baseball games around the country was selected. The speed of each pitch (in mph) is given in the table below.

a. Assume normality. Find a 95% confidence interval for the population mean speed of pitches in the first inning of Major League baseball games.

b. Find a 99% confidence interval for the population variance in speed of pitches in the first inning of Major League baseball games.

c. The mean speed of all pitches made in the first inning of games during the previous season was 90.225. Is there any evidence to suggest the mean speed has changed?