Question

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 167-lbs and a standard deviation of 26-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 5841-lbs.

Assume that there are 33 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 33 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded?
P(elevator overloaded) =  
(Report answer accurate to 4 decimal places.)

If the elevator is full (on average) 2 times a day, how many times will the elevator be overloaded in one (non-leap) year?
number of times overloaded =  
(Report answer rounded to the nearest whole number.)

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

Answer 1

The elevator will be overloaded if the total weight is in excess of 5841-lbs for 33 occupants (male)

a) the average weight beyond which the elevator would be considered overloaded =

The population of weights for men attending a local health club is normally distributed with a mean of -lbs and a standard deviation of lbs.

b) the probability that one randomly selected male health club member will exceed this weight =

c) the elevator will be overloaded if among the 33 in elevator the person is above 177 lbs

d)The expected number of times the elevator will be overloaded in one (non-leap) year = 2*366*0.0136=10(rounded up