The capacity of an elevator is 1515 people or 23852385 pounds. The capacity will be exceeded if 1515 people have weights with a
mean greater than 2385 divided by 15 equals 159 pounds.2385/15=159 pounds. Suppose the people have weights that are normally distributed with a mean of 165 lb165 lb and a standard deviation of 30 lb30 lb Find the probability that if a person is randomly selected, his weight will be greater than 159159 pounds.
We have been given that the capacity of an elevator is 15 people or 2385 pounds. The people have weights that are normally distributed with a mean of 165 lb and a standard deviation of 30 lb. We are asked to find the probability that a randomly selected person has a weight greater than 159 pounds.
First of all, we will find z-score corresponding to 159 using z-score formula.
Now, we need to find area under normal distribution curve that is greater than z-score of as:
Using formula , we will get:
Therefore, the probability that if a person is randomly selected, his weight will be greater than 159 pounds, is 0.57926.
If a triangle is inscribed in a circle, and its hypotenuse is the diameter, it is automatically a right triangle. Using the Pythagorean theorem, (diameter AB)^2 = (AC)^2 + (BC)^2 AB^2 = 144 + 25 = 169 AB = 13 Therefore the radius is 13/2 = 6.5 units.