Question 1174515: Urgent help needed. please help!!
NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem.
The population of weights for men attending a local health club is normally distributed with a mean of 169-lbs and a standard deviation of 30-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6370-lbs.
Assume that there are 35 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?
average weight =
lbs
What is the probability that one randomly selected male health club member will exceed this weight?
P(one man exceeds) =
(Report answer accurate to 4 decimal places.)
If we assume that 35 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded?
P(elevator overloaded) =
(Report answer accurate to 4 decimal places.)
If the evelator is full (on average) 6 times a day, how many times will the evelator be overloaded in one (non-leap) year?
number of times overloaded =
(Report answer rounded to the nearest whole number.)
Is there reason for concern?
no, the current overload limit is adequate to insure the safety of the passengers
yes, the current overload limit is not adequate to insure the safey of the passengers
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! average weight >182 lbs is the point for overloading.
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probability of 1 man being more than that is z >(182-169)/30 or z > 13/30 probability of 0.3324
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with 35 z =(182-169)/30/(sqrt(35), or z > 13*sqrt(*35)/30 or 2.56. That probability is 0.0052
2190 uses in a year
0.0052 probability of being overloaded
expected value of number of times is 11 times a year or almost once a month.
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Last question is not statistical. Given the issues of elevator safety, that appears to be more frequent than should be allowed, but one can argue from both sides.
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