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