Question

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 34 occupants, but it will be overloaded if the total weight is in excess of 6290-lbs.

Assume that there are 34 men in the elevator. What is the average weight of the 34 men 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 34 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) 7 times a day, how many times will the elevator be overloaded in one (non-leap) year?
number of times overloaded =

Answer 1

Average weight

Answer: average weight = 185 lbs.

Explanation:

The total weight (if overload) = 6290 lbs

Number of occupants = 34

P(one man exceeds)

Answer: P(one man exceeds) = 0.2969

Explanation: The population of weights for men is normally distributed with parameters, mean = 169 lbs and standard deviation = 30 lbs

The average weight if the elevator is overloaded = 185 lbs

The probability is obtained by calculating the z score,

From the z distribution table,

P(elevator overloaded)

Answer: P(elevator overloaded) 0.0009

Explanation: Now considering the sampling distribution of the weight with a sample size of 34,

The probability is obtained by calculating the z score,

From the z distribution table,

number of times overloaded

Answer: number of times overloaded = 2.3913

Explanation:

The number of days in a non-leap year = 365

The number of times an elevator is full in a day = 7

Total number of times an elevator is full in a non-leap year, n = 365*7 = 2555

The probability that the full elevator is overloaded, p = 0.000936

Expected number of times overloaded = n*p = 2555*0.000936 = 2.3913