The fielding percentage for a major league baseball team is a measure of how wel

Question

The fielding percentage for a major league baseball team is a measure of how well defensive players handle a batted ball(without error) and is based on total chances(putouts + assists + errors). One quarter into the 2013 baseball season, the Boston Red Sox fielding percentage was 0.984. Suppose 150 chances are randomly selected.

a.) Find the distribution of the sample proportion of chances handled without error.

b.) Find the probability that the sample portion is less than 0.97

c.) Find a value f such that P(Phat <= f ) = 0.05

d.) If the team fielding percentage for these random chances is greater than 0.99 then everyone on the team recieves a bonus. What is the probability of the team bonus?

Explanation / Answer

a This is proportional distribution with p=0.984 and n=150

b. P(x<0.97)=P(z<0.97-0.984/sqrt(0.984*(1-0.984)/150))=P(z<-1.367)=0.0858

c. P(F<=f)=0.05

Using z table we get z=-1.645=f-0.984/sd

So f=0.01*-1.645+0.984=0.967

d. P(x>0.99)=P(z>0.99-0.984/0.01)=P(z>0.586)=0.2789

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