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The maximum weight an elevator can take is 2500 pounds.

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

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,

\(\begin{array}{c}{\rm{Maximum}}\;{\rm{safe}}\;{\rm{load}} = 2500 + 625\\ = 3125\end{array}\)

Hence, the maximum safe load is 3125 pounds.

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.

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

\(\begin{array}{c}X \sim N\left( {{\mu _X} = 189,{\sigma _X}^2 = {{39}^2}} \right)\\Y \sim N\left( {{\mu _Y} = 171,{\sigma _Y}^2 = {{46}^2}} \right)\end{array}\)

Total 10 pounds are added for each students.

Thus, the change in random variables are,

\(\begin{array}{l}{X^'} = X + 10\\{X^'} \sim N\left( {{\mu _{{X^'}}} = 199,{\sigma _{{X^'}}}^2 = {{39}^2}} \right)\\{Y^'} = Y + 10\\{Y^'} \sim N\left( {{\mu _{{Y^'}}} = 181,{\sigma _{{Y^'}}}^2 = {{46}^2}} \right)\end{array}\)

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,

\(\begin{array}{c}n = \frac{{2500}}{{199}}\\ = 12.56\\ \approx 13\end{array}\)

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

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.