Major League Baseball now records information about every pitch thrown in every

Question

Major League Baseball now records information about every pitch thrown in every game of every season. 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. A histogram of speeds for all 30,740 four-seam fastballs thrown by these pitchers during the 2009 season is shown below, from which we can see that the speeds of these fastballs follow a Normal model with mean = 92.12 mph and a standard deviation of = 2.43 mph.

A baseball fan wishes to identify the four-seam fastballs among the fastest 22% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 22%? (Round your answer to the nearest 0.1 mph.)

__________________________ mph

Explanation / Answer

for fastest 22% at 78 th percentile z score =0.7712

therefore speed must a four-seam fastball be in order to be included in the fastest 22%

=mean +z*std deviaiton =92.12+0.7712*2.43 =94.0 mph

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