An elevator is rated to safely carry 5000 lbs. According to ABC News, the averag

Question

An elevator is rated to safely carry 5000 lbs. According to ABC News, the average American man weighs 195.7 lbs and the average woman 168.5 lbs. Assume that the people using this elevator are 58% men and 42% women. Assume that the population standard deviation is 31.2 lbs. What is the maximum number of people who can get on the elevator with a 99.5% probability that the total weight is safe? (Hint: for a random variable x with standard deviation , the standard deviation of nx is n.)

maximum safe number of riders: _________

Explanation / Answer

Ans:

mean weight=0.58*195.7+0.42*168.5=184.276

Mean for total carried weight of n people:

mean=184.76n

std. dev.=31.2n

z=normsinv(0.995)=2.58

2.58=(5000-184.276*n)/n*31.2

80.496n=5000-184.276*n

264.772n=5000

n=18.88

So,maximum safe number of riders is 18

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