Unit 6 Section 5.3 – Day 2

5.3: Normal Distributions: Finding Values Section 5.3 5.3: Normal Distributions: Finding Values Depending on what information is provided, using the Standard Normal Distribution table you can determine the following: A z-score, given the area A z-score, given a percentile An x-value, given a z-score A data value, given area or percentile

Section 5.3 Transforming a z-score into an x-value. Remember: Solve the equation for x.

Section 5.3 Example 1: a) A veterinarian records the weights of cats treated at a clinic. The weights are normally distributed, with a mean of 9 pounds and a standard deviation of 2 pounds. Find the weights (x) corresponding to z-scores of 1.96, -0.44, and 0.

Section 5.3 b) A teacher records the grades of a recent quiz into his grade book. The grades are normally distributed, with a mean of 86 and a standard deviation of 4 percent. Find the grades (x) corresponding to z-scores of 1.24, -0.34, and 2.00.

Section 5.3 Example 2: a) Scores for the Voorhees Township Officer Training test are normally distributed, with a mean of 50 and a standard deviation of 10. The department will only hire applicants with scores in the top 10%. What is the lowest score an applicant can earn and still be hired by the department?

Section 5.3 b) In a randomly selected sample of women aged 20 – 34, the mean total cholesterol level is 181 milligrams per deciliter with a standard deviation of 37.6 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a woman in this 20-34 age group can have and still be in the bottom 1%.

Classwork: Homework: Section 5.3 Complete: Practice 5.3 – Day 2 WS Pg 257-258: (31 – 38)