Question

The capacity of an elevator is 12 people or 2088 pounds. the capacity will be exceeded if 12 people have weights with a mean greater than 2088 divided by 12 equals 174 pounds. suppose the people have weights that are normally distributed with a mean of 177 lb and a standard deviation of 26 lb.

Answer 1

suppose the people have weights that are normally distributed with a mean of 177 lb and a standard deviation of 26 lb.

Find the probability that if a person is randomly selected, his weight will be greater than 174 pounds?

Assume that weights of people are normally distributed with a mean of 177 lb and a standard deviation of 26 lb.

Mean = 177

standard deviation = 26

We find z-score using given mean and standard deviation

z = $\frac{x-mean}{standard deviation}$

= $\frac{174-177}{26}$

=-0.11538

Probability (z>-0.11538) = 1 - 0.4562 (use normal distribution table)

= 0.5438

P(weight will be greater than 174 lb) = 0.5438