Question

bue in a hours, 24 minutes. Due Thu 01/24/2019 12:15 pm 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 165 lb and a standard deviation or 24 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario of 15 male passengers, find the maximum total allowable weight if we want a 0.975 probability that this maximum will not be exceeded when 15 males are randomly selected. maximum weight- lb Round to the nearest pound Answers obtained using exact 2-scores or z-scores rounded to 2 decimal places are accepted.

Answer 1

Let the variable X denotes weight of men.

The variable X follows Normal distribution with mean 165 lb and standard deviation 24 lb.

We have to find the maximum total allowable weight if we want 0.975 probability that this maximum will not be exceeded when 15 males are randomly selected.

That is we have to find $\bar{x}$ such that, $P(\bar{X}>\bar{x})=0.975$

Hence, $P(\bar{X}<\bar{x})=0.005$

That is, P(Z < z) = 0.005

Using standard normal table we find z score for the area 0.005.

Hence, z = 2.58

Therefore, $\bar{x}= \mu &plus;z*\sigma / \sqrt{n}$

$\bar{x}= 165&plus;2.58*24 / \sqrt{15}$

$\bar{x}= 180.9876 \approx 181$

Hence, maximum weight = 181 lb