The population of weights for men attending a local health club is normally dist

Question

The population of weights for men attending a local health club is normally distributed with a mean of 179-lbs and a standard deviation of 27-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 6208-lbs.

a. Assume that there are 32 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded? average weight = lbs

b. 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.)

c. If we assume that 32 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.)

d. If the elevator is full (on average) 8 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.)

e. 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 safety of the passengers

Explanation / Answer

given mean of 179-lbs and a standard deviation of 27-lbs

total weight is in excess of 6208-lbs.

number of occupants is 32

a) the elevator is overloaded if the total weight is over 6208,

so it's overloaded is the average is over 6208/32 = 194 lb.

b) now 194-179 = 15 lb above the mean. 15/27 = 0.5555 S.D

from standrad table pvalue = 1-0.7080=0.2920

c)  The S.D. for 32 randomly-selected men is 27 / sqrt(32) = 4.7730 lb. That makes the 15 pounds above mean equal to 15/4.7730 = 3.1426 S.D. above the mean on this distribution

from table 1-0.9992= 0.0008

d) The expected number of overloads is (number of trials)*P(overoad). The number of trials is 8 times the number of days in a year.

8*365* ( 0.0008) =2.336

so on average it overloads 2 to 3 times

e) no, the current overload limit is adequate to insure the safety of the passengers

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