Question

Problem #5: A fair 8-sided die is rolled 101 times. Consider the event A = {the face 2 comes up at most 2 times) (a) Find the normal approximation for P(A) without the continuity correction. (b) Find the normal approximation for P(A) with the continuity correction. (c) Find the Poisson approximation for P(A).

Answer 1

here for binomial distribution parameter n=101 and p=1/8

mean of distribution=μ=np=		12.63
and standard deviation σ=sqrt(np(1-p))=		3.3
for normal distribution z score =(X-μ)/σx

a)

probability =P(X<2)=(Z<(2-12.625)/3.324)=P(Z<-3.2)=0.0007

b)

probability =P(X<2.5)=(Z<(2.5-12.625)/3.324)=P(Z<-3.05)=0.0011

c)

this is Poisson distribution with parameter λ=12.625

P(X<=2)=

∑x=0x   {e-λ*λx/x!}=

0.0003