A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 180 lb and a standard deviation of 22 lb.

You need to design an elevator that will safely carry 19 people. Assuming a worst-case scenario of 19 male passengers, find the maximum total allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 19 males are randomly selected.

Round your answer to the nearest pound.

In this problem, we need to determine the maximum allowable total weight an elevator can carry given there are 19 male workers randomly selected. Normal distribution, mean, standard deviation, and z-scores play key roles in this calculation.

Firstly, we consider that men have a normally distributed weight with a mean of 180 lb and a standard deviation or 22 lb.

If we want a 0.995 probability that the maximum weight will not be exceeded when 19 males are randomly selected,

we need to look up the z value matching the 0.995 cumulative probability in a standard Z-table.

That z value is approximately 2.58. Multiply this by the standard deviation, then add the mean weight.

Multiply the result by 19 (the number of people). This gives you the maximum total allowable weight.

Mathematically, this should give you an answer approximately as follows: 19 * ((2.58 * 22) + 180) = 4088 lb.

So, the elevator should be designed to safely carry around 4088 lb to cover 99.5% of worst-case scenarios.

To know more about Probability visit:

brainly.com/question/12629667

#SPJ11