The population of weights for men attending a local health club is normally distributed with a mean of 172-lbs and a standard deviation of 27-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 6105-lbs. Assume that there are 33 men in the elevator.What is the average weight per man beyond which the elevator would be considered overloaded?average weight = lbs Round to the nearest pound.What is the probability that one randomly selected male health club member will exceed this weight?P(one man exceeds) = Round to 4 decimal places.If we assume that 33 male occupants in the elevator are a random sample of all male club members, find the probability that the elevator will be overloaded?P(elevator overloaded) = Round to 4 decimal places.If the elevator is full (on average) 2 times a day, how many times do we expect the elevator will be overloaded in one (non-leap) year?number of times overloaded = Round to the nearest day.Is there reason for concern?yes, the current overload limit is not adequate to insure the safey of the passengersno, the current overload limit is adequate to insure the safety of the passengers

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The population of weights for men attending a local health club is normally distributed with a mean of 172-lbs and a standard deviation of 27-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 6105-lbs. Assume that there are 33 men in the elevator.

What is the average weight per man beyond which the elevator would be considered overloaded?

average weight = lbs Round to the nearest pound.
What is the probability that one randomly selected male health club member will exceed this weight?

P(one man exceeds) = Round to 4 decimal places.
If we assume that 33 male occupants in the elevator are a random sample of all male club members, find the probability that the elevator will be overloaded?

P(elevator overloaded) = Round to 4 decimal places.
If the elevator is full (on average) 2 times a day, how many times do we expect the elevator will be overloaded in one (non-leap) year?

number of times overloaded = Round to the nearest day.

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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