A telephone company's goal is to have no more than 6 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 line. (Do not round intermediate calculations. Round final answer to 4 decimal places.) |
A telephone company's goal is to have no more than 6 monthly line failures on any 100 miles of line
That is company meets its goal if failure are less than equal to 6
We have to calculate P(X <= 6) = ?
X ~ poi ( )
Where = 2 failures per 50 miles of line
For 100 miles of line,
= 2 * 100 / 50 = 4
Using EXCEL,
P(X <= x) = POISSON.DIST ( x , mean , cumulative)
So,
P(X <= 6) = POISSON.DIST ( 6 , 4 , TRUE )
= 0.8893
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