The empirical rule, also sometimes called the three-sigma or 68-95-99.7 rule, is a statistical rule

Description

A bone mineral density test can help identify the likelihood of osteoporosis, a disease causing bones to become more fragile and more likely to break.

The result of a bone density test is commonly measured as a z score. The population of z scores is normally distributed with a mean of zero and a standard deviation of one. Therefore these tests meet the requirement of a standard normal distribution and the graph of bone density is a bell-shaped normal distribution curve.

Questions: A randomly selected adult undergoes a bone density test.

Question #1)

Find the probability that this person has a bone density test less than 1.27. Show your work, and explain your solution.

Question #2)

Find the probability that this person has a bone density test of more than 1.27. Show your work, and explain your solution.

Question #3)

Find the probability that this person has a bone density test z = -1. Show your work.

Question #4)

Explain your solution step by step for question #3.