Question

Statistician Jim Albert compiled data about every pitch thrown by 20 starting pitchers during the 2009 MLB season. The data set included the type of pitch thrown (curveball, changeup, slider, etc.) as well as the speed of the ball as it left the pitcher's hand. The data showed that the speeds of the fastballs are normally distributed with mean 92.12 mph and standard deviation 2.43 mph.

(a) Compute the z-score of the fastball with speed 91.4 mph. Round your answer to two decimal places

(b)What percentage of these fastballs would you expect to have speeds between 91.3 mph and 93.9 mph? Express your answer as a decimal. Round to three decimal places.

(c)What percentage of these fastballs would you expect to have speeds above 93.9 mph? Express your answer as a decimal. Round to three decimal places.

(d)Finding Values: A baseball fan wishes to identify the fastballs among the fastest 3% of all such pitches. Above what speed must a fastball be in order to be included in the fastest 3%? Round your answer to the nearest 0.1 mph.

Answer 1