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 |
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