1: 2: Major League Baseball now records information about every pitch thrown in

Question

1:

2:

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.

An electronic product takes an average of 7 hours to move through an assembly line. If the standard deviation of 0.8 hours, what is the probability that an item wil take between 7.4 and 9.1 hours to move through the assembly line? Do not round until you get your your final answer Answer (Round your answer to 4 decimal places, and report a probability value between 0 and 1.) Warning: Do not use the Z Normal Tables...hey may not be accurate enough since WAMAP may look for more accuracy than comes from the table.

Explanation / Answer

1) P(7.4<X<9.1)=P(0.5<Z<2.625)=0.9957-0.6915 =0.3042

2)

a)z score =(X-mean)/std deviation =(88.1-92.12)/2.43=-1.65

b)

P(91.3<X<92.7)=P(-0.3374<Z<0.2387)=0.5943-0.3679 =0.2264

c) P(X>92.7)=P(Z>0.2387)=0.4057

d)for fastest 13% ; z =1.1264

hence corresponding speed =mean+z*std deviaiton =94.9

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