41. Here are the lengths (in minutes) of the 63 nineinning games from the rst week of the 2001 major league baseball season:

194 160 176 203 187 163 162 183 152 177 177 151 173 188 179 194 149 165 186 187 187 177 187 186 187 173 136 150 173 173 136 153 152 149 152 180 186 166 174 176 198 193 218 173 144 148 174 163 184 155 151 172 216 149 207 212 216 166 190 165 176 158 198 Assume that this is a random sample of nine-inning games (the mean differs by 12 seconds from the mean for the whole season).

a. Give a 95% con dence interval for the population mean.

b. Give a 95% prediction interval for the length of the next nine-inning game. On the rst day of the next week, Boston beat Tampa Bay 3-0 in a nineinning game of 152 minutes. Is this within the prediction interval?

c. Compare the two intervals and explain why one is much wider than the other.

d. Explore the issue of normality for the data and explain how this is relevant to parts

(a) and (b).