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A telephone company's goal is to have no more than five monthly line failures on any 100 miles of line. The company currently experiences an average of two 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.
b. Find the probability that the company will not meet its goal on a particular 100 miles of line.
c. Find the probability that the company will have no more than five monthly failures on a particular 200 miles of line.
d. Find the probability that the company will have more than 12 monthly failures on a particular 150 miles of line.
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