A courier company owns 87 delivery trucks. On average, on any given day 5% of th

Question

A courier company owns 87 delivery trucks. On average, on any given day 5% of these trucks are in for repair. Assume that trucks break down independently and that repairs take only one day to carry out. What is the expected number of trucks in for repair on any given day? What is the standard deviation of the number of trucks in for repair on any given day? What is the probability that at least three trucks will be in for repair on any given day? What is the probability that in an entire workweek (5 days) two of the days will have at least 3 trucks in for repairs?

Explanation / Answer

c) instead of approximation use actual distribution binomial P(x>=3)=1-p(X=0)-P(X=1)-P(X=2) =1-C(87,0).05^0(.95^87)-C(87,1)(.05^1)(.95^86)-C(87,2) (.05^2)(.95^85)=.8161 d) this is also a binomial distribution with p=.8161,n=5 ans =C5,2)(.8161^2)(.1839^3)=.041241889

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