Assume the average baseball player has about 600 plate appea

Assume the average baseball player has about 600 plate appearances and a batting average of .250 in a season. Using the Normal Approximation to the binomial, answer the following questions?

Part A :
Average number of hits in a season
Part B:
Probability of having more than 180 hits in a season
Part C:
Probability of having less than 100 hits in a season

Solution

Part A : Average number of hits in a season

average= n*p = 600*0.25 =150

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Part B: Probability of having more than 180 hits in a season

standard deviation =sqrt(n*p*(1-p))

=sqrt(600*0.25*0.75)

=10.6066

So the probability is

P(X>180) = P((X-mean)/s >(180-150)/10.6066)

=P(Z>2.83) =0.0023 (from standard normal table)

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Part C: Probability of having less than 100 hits in a season

P(X<100) = P(Z<(100-150)/10.6066)

=P(Z<-4.71) =0 (from standard normal table)