A telephone company\'s goal is to have no more than 4 monthly line failures on a

Question

A telephone company's goal is to have no more than 4 monthly line failures on any 100 miles of line. The company currently experiences an average of 3 monthly line failures per 50 miles of line. Let x denote the number of monthly line failures per 100 miles of line. Assuming x has a Poisson distribution: (a) Find the probablity that the company wil meet lts goal on a particular 100 mles of lne. (Do not round Intermediate calculations. Round final answer to 4 declmal places.) Probabillty (b) Find the probability that the company will not meet its goal on a particular 100 miles of line. (Do not round intermediate calculations. Round final answer to 4 decimal places.) Probability (c) Find the probabllity that the company will have no more than 4 monthly failures on a particular 200 miles of line. (Do not round intermediate calculations. Round final answer to 4 decimal places.) Probability (d) Find the probability that the company will have more than 12 monthly failures on a particular 150 miles of line. (Do not round intermediate calculations. Round final answer to 4 decimal places.) Probability 1738

Explanation / Answer

Ans:

a)Average monthly failure per 100 miles=6

P(meet goal)=P(x<=4)=e-6*(60/0!+61/1!+62/2!+63/3!+64/4!)

=e-6*(1+6+18+36+54)=0.2851

b)P(not meet goal)=P(x>4)=1-P(x<=4)=1-0.2851=0.7149

c)average number of failures on 200 miles=3*4=12

P(x<=4)=e-12*(120/0!+121/1!+122/2!+123/3!+124/4!)

=e-12*(1+12+72+288+864)

=0.0076

d)average number of failures on 150 miles=3*3=9

P(x>12)=1-P(x<=12)=1-poisson(12,9,true)=1-0.8758=0.1242

(use excel function poisson)

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