Question

Assume a binomial probability distribution with n=40 and π = .55. Compute the following:

1. The mean and standard deviation of the random variable.
2. The probability that X is 25 or greater
3. The probability that X is 15 or less.
4. The probability that X is between 15 and 25 inclusive.

Answer 1

a)

mean of distribution=μ=np=

22.00

standard deviation σ=√(np(1-p))=

3.1464

b)

probability =

P(X>=25)=

1-P(X<=24)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.2142

c)

probability =

P(X<=15)=

∑x=0x     (nCx)px(1−p)(n-x)    =

0.0196

d)

probability =

P(15<=X<=25)=

∑x=x1x2     (nCx)px(1−p)(n-x)    =

0.8588