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Subway escalators. The city of Hyperion has a hyper-fast service crew that can repair subway escalators...

Subway escalators. The city of Hyperion has a hyper-fast service crew that can repair subway escalators the evening after an escalator breaks. (If only our Metro system could hire them!) Hyperion has 20 escalators on its subway system. Each escalator has a probability of 1 percent (0.01) of not working properly on any given day. The probability of any one escalator breaking is stationary over time and independent of whether it breaks on any other day and independent of the probability of any other escalator breaking.

At the end each problem, round to 4 digits past the decimal.

A. Use the binomial distribution to calculate the probability that 1 of the 20 escalators will not work properly today.

B. Use the Poisson approximation to the binomial distribution to calculate the probability that 1 of the 20 escalators will not work properly today.

C. I care most the subway stop closest to my house where I get on. What is the probability that its escalator will be working for 5 days, Monday through Friday, without breaking once to get me through my workweek?

Math   Statistics-And-Probability   
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