Ergonomics. Exercises 9–16 involve applications to ergonomics,...

Question

Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.

Safe Loading of Elevators The elevator in the car rental building at San Francisco International Airport has a placard stating that the maximum capacity is “4000 lb—27 passengers.” Because 4000/27=148, this converts to a mean passenger weight of 148 lb when the elevator is full. We will assume a worst-case scenario in which the elevator is filled with 27 adult males. Based on Data Set 1 “Body Data” in Appendix B, assume that adult males have weights that are normally distributed with a mean of 189 lb and a standard deviation of 39 lb.

a. Find the probability that 1 randomly selected adult male has a weight greater than 148 lb.

Accepted Answer

Hello. In this video, we're told that a theme park ride has a sign stating the maximum capacity is 3200 pounds per 20 riders. This means that the average rider weight should be, should not exceed 160 pounds when the ride is full. Suppose the ride is filled with 20 adult males. Assume adult male weights are normally distributed with the mean of 180 pounds and a standard deviation of 25 pounds. What is the probability that a randomly selected adult male weighs more than 160 pounds? So let's just go ahead and list out some given information. First we are told that we have a mean. of 180. We are also told that we have a standard deviation of 25, and our goal is to determine the probability that a randomly selected male weighs more than 160 pounds. So, in order to approach this problem, let's go ahead and convert our probability into a Z score. Now, the Z score is defined as the following. It's the value of X we're interested in minus our mean divided by the standard deviation. In this case here, this is going to be 160 minus 180 divided by 25, and this is going to simplify to be negative 0.8. So we can rewrite our probability. To be that we want to find the probability that Z is greater than negative 0.8. Now, this is equivalent to finding 1 minus the probability that Z is less than 0.8, and by using the Z table in the appendix, we are able to translate this probability to be 1 minus 0.2119, which will simplify to be 0.7881. Now, what this means is that the probability that a randomly selected male weighs more than 160 pounds, is about 78.81%. And with that being said, the solution to this problem is going to be B. So, I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

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Key Concepts

Normal Distribution

Z-Score

Probability Calculation

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