If n5 and 040 what is the probability that a X4 b X 3 c X 2

If n=5 and =0.40, what is the probability that:

a. X=4

b. X 3

c. X 2

d. X 1

Show the excel formulas used to solve for each one.

Solution

Given n=5, p=0.4, so we use binomial distribution P(X=4)=(5c4)*((.4)^4)*((1-0.6)^(5-4))=0.0768. P(X 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=(5c0)*((.4)^0)*((1-0.6)^(5-0))+(5c1)*((.4)^1)*((1-0.6)^(5-1))+(5c2)*((.4)^2)*((1-0.6)^(5-2))+(5c3)*((.4)^3)*((1-0.6)^(5-3))=0.0778+0.2592+0.3456+0.2304=0.913. P(X<2)=P(X=0)+P(X=1)=(5c0)*((.4)^0)*((1-0.6)^(5-0))+(5c1)*((.4)^1)*((1-0.6)^(5-1))=0.0778+0.2592=0.337. P(X>1)=1-P(X<=1)=1-[P(X=0)+P(X=1)]=1-[0.337]=0.663.