Question

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?

a) 0.93

b) 0.9693

c) 0.07

d) 0.0307

Answer 1

Answer:

here for binomial distribution parameter n=800 and p=0.07

here mean of distribution=μ=np=	56.00
and standard deviation σ=sqrt(np(1-p))=	7.22
for normal distribution z score =(X-μ)/σx
since np and n(1-p) both are greater than 5, we can use normal approximation of binomial distribution

probability that this baseball player hits at most 42 home runs in 800 at-bats :

probability =P(X<42.5)=(Z<(42.5-56)/7.217)=P(Z<-1.87)=0.0307

Option D is Correct

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