37 Orings Failures of Orings on the space shuttle were fairl

37. O-rings Failures of O-rings on the space shuttle were fairly rare, but could be disastrous, events. If we were testing O-rings. suppose that the probability of a failure of any one O-ring is 0.01. Let X be the number of failures in the nest 10 O-rings tested. a) What model might you use to model X? b) What is the mean number of failures in the next 10 O-rings? c) What is the probability that there is exactly one failure in the next 10 O-rings? d) What is the probability that there is at least one failure in the next 10 O-rings?

Solution

(a) X follows Binomial distriubtion with n=10, p=0.01

P(X=x)=10Cx*(0.01^x)*(0.99^(10-x)), for x=0,1,...,10

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(b) mean=n*p=10*0.01=0.1

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(c) The probability is

P(X=1)=10C1*(0.01^1)*(0.99^(10-1))=0.09135172

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(d) The probability is

P(X>=1)=1-P(X=0)

=1-10C0*(0.01^0)*(0.99^(10-0))

=0.09561792