Major League Baseball now records information about every pitchthrown in every game of every season. Statistician Jim Albertcompiled data about every pitch thrown by 20 starting pitchersduring the 2009 MLB season. The data set included the type of pitchthrown (curveball, changeup, slider, etc.) as well as the speed ofthe ball as it left the pitcher’s hand. A histogram of speeds forall 30,740 four-seam fastballs thrown by these pitchers during the2009 season is shown below, from which we can see that the speedsof these fastballs follow a Normal model with mean μ = 92.12 mphand a standard deviation of σ = 2.43 mph.

Compute the z-score of pitch with speed 88.9 mph. (Roundyour answer to two decimal places.)



Approximately what fraction of these four-seam fastballs would youexpect to have speeds between 89.1 mph and 92.5 mph? (Express youranswer as a decimal, not a percent, and round to three decimalplaces.)



Approximately what fraction of these four-seam fastballs would youexpect to have speeds below 89.1 mph? (Express your answer as adecimal, not a percent, and round to three decimal places.)



A baseball fan wishes to identify the four-seam fastballs among thefastest 3% of all such pitches. Above what speed must a four-seamfastball be in order to be included in the fastest 3%? (Round youranswer to the nearest 0.1 mph.)

mph