Show work City planners estimate that they can attract 20% of commuters who curr

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City planners estimate that they can attract 20% of commuters who currently use bus service to a new light rail to the downtown area. Suppose that 72000 independent commuters use bus service daily (a) Approximate the probability that more than 10800 commuters will use the light rail daily, Round your answer to three decimal places (e.g. 98.765) (b) Approximate the number of daily commuters who will use the light rail which will be exceeded with probability only 0.05 Round your answer to the nearest integer (e.g. 9876) The number of daily commuters who will use the light rail which will be exceeded with probability only 0.05 is

Explanation / Answer

Total customers that can be attracted = 20% of 72000

= 0.2*72000 = 14400

a)

P(more than 10800 commuters will use the light rail daily) = 1 - P(less than or equal to 10800 commuters will use light rail daily)

= 1 - 10800/14400

= 1 - 0.75

= 0.25

b)

Number of daily commuters who will use light rail which will be exceeded with probability only 0.05

= 0.05 * 72000 = 3600

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