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 at most 42 home runs in 800 at-bats?

0.0307

0.9693

0.93

0.07

Answer 1

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