Suppose that for a single launches of a space shuttle there

Suppose that for a single launches of a space shuttle there is a constant probability of o-ring failure(say,.15) consider ten future launches, and let x be the number of those involving an o-ring failure. use an appropriate probability model and evaluate all of the following.

A. P[X=2]

C.EX

D. Var X

E. the standard deviation of X

Solution

This is a binomial distirbution, n=10

p=0.15

a)P(x=2)=0.2759

use BINOM.DIST function in excel.

b)P(x>=11)=1-P(x<11)

this is x=0,1,2...10

this is the whole pmf and it is 1.

so P(x>=11)=1-1=0

c) E(X)=np=10*0.15=1.5

d) V(X)=npq=10*0.15*0.85=1.275

e) sd(x)=sqrt(V(x))=sqrt(1.275)=1.1291