A telephone company\'s goal is to have no more than 5 monthly line failures on a

Question

A telephone company's goal is to have no more than 5 monthly line failures on any 100 miles of line. The company currently experiences an average of 2 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 probability that the company will meet its goal on a particular 100 miles of the. (Do not round intermediate calculations. Round final answer to 4 decimal places.) Probability 8902 (b) Find the probability that line 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 probability that the company will have no more than 6 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 _______

Explanation / Answer

u = 4

a)

P(X < =6)

= POISSONDIST( 6, 4, TRUE)

= 0.8893

b)

P(X > 6) = 1- P(X <=5)

= 0.1107

c)

u = 8

P(X <=6) = POISSONDIST( 6, 8 , TRUE)

= 0.3133

d)

u = 6

P(X > 12) = 1 - P(X < 12)

= 1 - POISSONDIST( 12, 6, TRUE)

= 1 - 0.9912

= 0.0088

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