Chapter 6: Q1 (page 295)

Designing a campus dormitory elevator, an Ohio college student died. He tried to escape from a dormitory elevator overloaded with 24 passengers. The elevator could hold a maximum weight of 2500 pounds. Let’s consider parameters for weights of adults, as shown in the given table (based on Data Set 1 “Body Data” in Appendix B).
Weights of the adults:
Males
Females
$μ$
189lb
171lb
$σ$
38lb
46lb
Distribution
Normal
Normal
We could consider design features such as the type of music that could be played on the elevator. We could select songs such as “Imagine,” or “Daydream Believer.” Instead, we will focus on the critical design feature of weight.
a.First, elevators commonly have a 25% margin of error, so they can safely carry a load that is 25% greater than the stated load. What amount is 25% greater than 2500 pounds? Let’s refer to this amount as “the maximum safe load” while the 2500 pound limit is the “placard maximum load.”
b.Now we need to determine the maximum number of passengers that should be allowed. Should we base our calculations on the maximum safe load or the 2500 pound placard maximum load?
c.The weights given in the accompanying table are weights of adults with no clothing, a circumstance not totally unheard of in college dormitory experiences. Add another 10 pounds for each student’s clothing and textbooks (I know, I know). What is the maximum number of elevator passengers that should be allowed?
d. Do you think that weights of college students are different from weights of adults from the general population? If so, how? How would that affect the elevator design?

Short Answer

Expert verified

a.The 25% greater than 2500 pounds is equal to 3125 pounds.

b.To determine the maximum number of passengers that should be allowed, we should base our calculations on the 2500 pounds placard maximum load.

c. The total number of passengers allowed is 13.

d. Yes, the elevator should be designed with more capacity.

Step by step solution

Given Information

The maximum weight an elevator can take is 2500 pounds.

The distribution of weights for adults; males and females is known.

Compute the maximum safe load

a. The margin of error 25% equals to 0.25.

The maximum safe load is 25% greater than the stated load value.

Now 25% of 2500 pounds is given by,

$0.25 \times 2500 = 625$

Therefore, the amount computed as 25% greater than 2500 is,

$Maximum safe load = 2500 + 625 = 3125$

Hence, the maximum safe load is 3125 pounds.

Identify the permissible load

b. As the stated, load limit is 2500 pounds and 3125 is the maximum load that could be taken by the elevator. The value 2500 pounds must be taken for calculations to maintain the safety standards in elevators.

Calculate the number of passengers

c. Let X be the weight of males and Y be the weights for females.

$X ~ N (μ_{X} = 189, {σ_{X}}^{2} = 39^{2}) Y ~ N (μ_{Y} = 171, {σ_{Y}}^{2} = 46^{2})$

Total 10 pounds are added for each students.

Thus, the change in random variables are,

$X^{'} = X + 10 X^{'} ~ N (μ_{X^{'}} = 199, {σ_{X^{'}}}^{2} = 39^{2}) Y^{'} = Y + 10 Y^{'} ~ N (μ_{Y^{'}} = 181, {σ_{Y^{'}}}^{2} = 46^{2})$

The maximum mean weight for any passenger is 199 lb in males.

The maximum allowed load is 2500 lb.

Thus, the total number of passengers allowed are,

$n = \frac{2500}{199} = 12.56 \approx 13$

Therefore, total number of passengers that must be allowed are 13.

Conclusion About the Weights

d. Yes, there exists a difference in weights between college student and adults. College students normally posses less weight as compared to an adult. The elevator should be designed with more capacity.