Question
In: Statistics and Probability
The population of weights for men attending a local health club is normally distributed with a...
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 =
Solutions
Expert Solution
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
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