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 7 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 line. (Do not round intermediate calculations. Round final answer to 4 decimal places.)

Probability            

(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 probability that the company will have no more than 5 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

a) Given,

Average = 7 per 50 miles of line = 14 per 100 miles of line

So,

P(Meeting goal)

P(X < 5)

= 0.0055

b) P(Not meeting its goal)

= 1 - P(Meeting its goal)

= 1 - 0.0055

= 0.9945

c) For 200 meters of line, average failures = 7*4 = 28

So,

P(x < 5)

= 0.0000

d) For 150 miles of line, average failures = 7*3 = 21

So,

P(X > 12)

= 1 - P(X < 12)

= 1 - 0.0245

= 0.9755

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