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 μ = 91.64 mph and σ = 2.82 mph. Approximately what proportion of these four-seam fastballs would you expect to have speeds between 88.7 mph and 93.1 mph? (Express your answer as a decimal and round to 4 decimal places.)
Approximately what proportion of these four-seam fastballs would you expect to have speeds below 88.7 mph? (Express your answer as a decimal and round to 4 decimal places.)
A baseball fan wishes to identify the four-seam fastballs among the fastest 18% of all such pitches. Above what speed must a four-seam fastball be in order to be included in the fastest 18%? (Round your answer to the nearest 0.1 mph.)