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 p - 92.12 mph and a standard deviation of o = 2.43 mph. 000 $ 000 50 speed

Answer 1

let X: four-seam fugtballs speeds Xn Nonnal ( M = 92.12 , 8=2.43) a) Zscon= X-4 X-4 Zabu = - 1.7613 1.76 ✓ 96.4 - 92.12 2.49 pl gol LaL 94.9 ] =P ( 90.1-92-12 La-l L 94.9-92.12 2.43 6 2.49 P 1-0.8313 LZL - 1.1440 0.6708 ✓ 0.671 V P(Z L-0.8313 i pc ncgo 1] = 0.2029 ✓ Z 0.203 ✓ Ex) PLX festest ] = 0.23 J-o 23y Z АРГ z > X fastest - 92.12 =0.23 PL 2.43 Using Il fastest - 92.12 -0.739 2-43 Xfastest 93 91577 2 table 005733 a 93.9 mph