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There are a number of different suburban lines in Mumbai, some of which meet at a common station. At one such station, Dadar, the builders want to accommodate passenger flow across the Central and Western lines by building a bridge between each terminus. The bridge is designed to typically carry two people side by side, but during rush hour it sees up to three people squeeze into one row, rushing to get to the other end. At a given point of time eighty such rows of commuters are seen jostling on the bridge. The population of passengers at rush hour is almost exclusively made up of adult men and women, whose weight is normally distributed with an average of about 65 kg with a standard deviation of about 15 kg. A) B) If the bridge’s beams can hold a weight of 16 metric tons before they start to bend (this is safe but creates panic among the passengers), how often would you expect the bridge to sag? (Express your answer in the form "about 1 in every n days") Given that the morning and evening peak traffic periods together last about an hour and a half, and the turnover on the bridge is such that it's like having a new trip with 240 new people about every minute during this period, do you regard the bridge’s frequency of sagging as acceptably low? C) If the engineers had wanted the bridge’s beams to bend only about once a year, how much weight should they have designed it to carry?

There are a number of different suburban lines in Mumbai,
some of which meet at a common station. At one such
station, Dadar, the builders want to accommodate passenger
flow across the Central and Western lines by building a
bridge between each terminus. The bridge is designed to
typically carry two people side by side, but during rush hour
it sees up to three people squeeze into one row, rushing to
get to the other end. At a given point of time eighty such
rows of commuters are seen jostling on the bridge. The
population of passengers at rush hour is almost exclusively
made up of adult men and women, whose weight is
normally distributed with an average of about 65 kg with a
standard deviation of about 15 kg.
A)
B)
If the bridge’s beams can hold a weight of 16 metric
tons before they start to bend (this is safe but creates
panic among the passengers), how often would you
expect the bridge to sag? (Express your answer in the
form "about 1 in every n days")
Given that the morning and evening peak traffic
periods together last about an hour and a half, and the
turnover on the bridge is such that it's like having a new
trip with 240 new people about every minute during
this period, do you regard the bridge’s frequency of
sagging as acceptably low?
C)
If the engineers had wanted the bridge’s beams to
bend only about once a year, how much weight should
they have designed it to carry?

Grade:12

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