A telephone company\'s goal is to have no more than 3 monthly line failures on a
ID: 3360076 • Letter: A
Question
A telephone company's goal is to have no more than 3 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 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 3 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
P(X=x) = e^-u u^x/x!
=>
a)
P(X <=3)
= e^-6 ( 1+ 6 + 6^2/2! + 6^3/3! )
= 0.1512
b)
P(X > 3) = 1- P(X <=3)
= 1 - 0.1512
= 0.8488
c)
P(X <=3)
= e^-12 ( 1+ 12 + 12^2/2! + 12^3/3! )
= 0.0002
d)
P(X >12)
= 1- P(X<=12)
= 1 - e^-9( 1 + 9 + 9^2/2 + 9^3/6 + 9^4/24 + 9^5/120 + 9^6/720 + 9^7 /5040 + 9^8/40320 + 9^9/362880 + 9^10/3628800 + 9^11/39916800 + 9^12/479001600)
= 1 - 0.8758
= 0.1242
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