Normal Probability Help: steep escalator at Pimlico station

JohnDwyer

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Jul 21, 2016
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I am struggling a little with this problem and need some advice if I am going in the right direction and specifically Task 4 which really didn't make sense. Here are the tasks I have attached a pic with the data from the question which was too long to type

Task 1: If the engineers designed the escalator to perform properly with a maximum total load of 29,700 pounds, what is the average weight per person allowed during rush hour?
29700 max weight / 192 max # of people = 154.69 avg weight/person at rush hour.

Task 2: What is the probability that the maximum load will be exceeded during rush hour?

154.69-150/28 = .1675 Z score = 56.65% chance of failure at rush hour

Task 3: Express your answer in task 2 as a fraction

1133 failures / 2000 trips

Task 4:
Given that rush "hour" lasts about 90 min and that these conditions are like a turnover on the escalator of a new trip every single minute, how many turnovers are there during the rush period?
I feel like it should be 90 turnovers, but that seems way to simple @ 90min and 1 per min. Not very overly complicated statistic like.

Task 5: Would you be surprised for the escalator to stop working properly during the rush hour traffic? Why or why not?
No, I would not be surprised if the escalator were to stop working properly during rush hour traffic with the a 56.65% chance of the of the maximum load being exceed during this time. This gives it a greater than 50% chance of not performing properly.
 

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For other viewers, this is the text of the exercise:



There are many subway ("tube") lines in London. Some of them had to be built parallel to each other, or "stacked", below ground. To get to the deeper lines, you have to ride down on very long and pretty steep escalators. A the Pimlico station, the escalator is like a moving staircase with 96 steps. During the rush periods of the day, there are usually two people on each step of the escalator. So the escalator must be designed to accommodate 192 people without overloading.

Assume that the most severe load is at "rush hour" of 90 minutes duration, and that the escalator passengers are adults with an average weight of 150 pounds and standard deviation of 28 pounds. Further assume that these weights are normally distributed. Based on this information, complete the following tasks:
 
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