Question

Your computer randomly generates numbers in the set { 1,2,3,4,5 }. Each outcome is equally likely each time you compute a random number. ( It's a uniform distribution. ). You randomly generate 100 numbers and will win a prize if 19% or more of your randomly generated numbers is a 2. Find the probability that you win.

Answer 1

here for binomial distribution number of trails n=100 and probabiltiy of getting a 2 on one trail=1/5=0.2

here mean of distribution=μ=np=		20.00
and standard deviation σ=sqrt(np(1-p))=		4.00
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

  probability that you win (getting 19 or more 2 in 100):

probability =P(X>18.5)=P(Z>(18.5-20)/4)=P(Z>-0.38)=1-P(Z<-0.38)=1-0.352=0.6480