Question

Everyday Jo practices her tennis serve by continually serving until she has had a total of 50 successful serves. If each of her serves is, independently of previous ones, successful with probability 0.4, approximately what's the probability that she will need more than 100 serves to accomplish her goal? Please solve this problem by using normal approximation of binomial distribution only. (Hint: Imagine even if Jo is successful that she continues to serve until she has served exactly 100 times. What must be true about her first 100 serves if she's to reach her goal?)

Answer 1

n=	100	p=	0.4000
here mean of distribution=μ=np=		40
and standard deviation σ=sqrt(np(1-p))=		4.8990

for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution :

probability that she will need more than 100 serves to accomplish her goal =P(at most 49 successful serves in 100 total surves)

P(X<=49)=P(Z<(49.5-40)/4.899)=P(Z<1.94)=0.9738

(try 0.9671 or 0.9793 if above comes wring and revert)