The population of weights for men attending a local health club is normally distributed with a mean of 172-lbs and a standard deviation of 27-lbs. An elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 6105-lbs. Assume that there are 33 men in the elevator.What is the average weight per man beyond which the elevator would be considered overloaded?average weight = lbs Round to the nearest pound.What is the probability that one randomly selected male health club member will exceed this weight?P(one man exceeds) = Round to 4 decimal places.If we assume that 33 male occupants in the elevator are a random sample of all male club members, find the probability that the elevator will be overloaded?P(elevator overloaded) = Round to 4 decimal places.If the elevator is full (on average) 2 times a day, how many times do we expect the elevator will be overloaded in one (non-leap) year?number of times overloaded = Round to the nearest day.Is there reason for concern?yes, the current overload limit is not adequate to insure the safey of the passengersno, the current overload limit is adequate to insure the safety of the passengers

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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The population of weights for men attending a local health club is normally distributed with a mean of 172-lbs and a standard deviation of 27-lbs. An elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 6105-lbs. Assume that there are 33 men in the elevator.

What is the average weight per man beyond which the elevator would be considered overloaded?

average weight = lbs Round to the nearest pound.
What is the probability that one randomly selected male health club member will exceed this weight?

P(one man exceeds) = Round to 4 decimal places.
If we assume that 33 male occupants in the elevator are a random sample of all male club members, find the probability that the elevator will be overloaded?

P(elevator overloaded) = Round to 4 decimal places.
If the elevator is full (on average) 2 times a day, how many times do we expect the elevator will be overloaded in one (non-leap) year?

number of times overloaded = Round to the nearest day.

Is there reason for concern?
- yes, the current overload limit is not adequate to insure the safey of the passengers
- no, the current overload limit is adequate to insure the safety of the passengers