Question

Let's say the probability that a Major league baseball player hits a homerun is 0.099. What is the probability that he hits exactly 40 homeruns in his next 500 at bats?  

Answer 1

n=

500

p=

0.0990

here mean of distribution=μ=np=		49.50
and standard deviation σ=sqrt(np(1-p))=		6.68
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability that he hits exactly 40 home runs in his next 500 at bats :

probability =P(39.5<X<40.5)=P((39.5-49.5)/6.678)<Z<(40.5-49.5)/6.678)=P(-1.5<Z<-1.35)=0.0885-0.0668=0.0217