Question

The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning at least 30 times. (A) Almost 0 B) Between 0.01 and 0.20 (C) Between 0.20 and 0.40 (D) Between 0.40 and 0.60 (E) Greater than 0.60

Answer 1

n=	500	p=	0.0500
here mean of distribution=μ=np=		25
and standard deviation σ=sqrt(np(1-p))=		4.8734
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

P(winning at least 30 times):

probability =

P(X>29.5)

=

P(Z>0.92)=

1-P(Z<0.92)=

1-0.8212=

0.1788

option B is correct between 0.01 and 0.20