Essential Questions

1. Essential Questions • How do we use tables to estimate areas under normal curves? • How do we recognize data sets that are not normal?

2. + 3s – s – s + s – 2s + 2s + 3s – 3s – 3s + 2s – 2s + s x x x x x x x x x x x x x Standard Deviation of a Data Set A normal distribution with mean x and standard deviation s has these properties: 1 • The total area under the related normal curve is ____. 68 • About ___% of the area lies within 1 standard deviation of the mean. 95 • About ___% of the area lies within 2 standard deviation of the mean. 99.7 • About _____% of the area lies within 3 standard deviation of the mean. 34% 34% 68% 13.5% 13.5% 95% 2.35% 2.35% 99.7% 0.15% 0.15% x

3. – s + s – 2s + 2s – 3s + 3s x x x x x x x Find a normal probability A normal distribution has a mean x and standard deviation s. For a randomly selected x-value from the distribution, find

4. Interpret normally distributed data The math scores of an exam are normally distributed with a mean of 518 and a standard deviation of 115. About what percent of the test-takers have scores between 518 and 748? 633 748 173 288 403 518 863 About what percent of the test-takers have scores less than 403? About what percent of the test-takers have scores between 403 and 633?

5. Interpret normally distributed data The heights (in feet) of fully grown white oak trees are normally distributed with a mean of 90 feet and a standard deviation of 3.5 feet. About what probability of white oak trees have heights between 86.5 feet and 93.5 feet? 93.5 97 79.5 83 90 100.5 86.5 About what probability of white oak trees have heights between 79.5 feet and 86.5 feet? About what probability of white oak trees have heights greater than 93.5 feet?

6. Lesson 2.3 Practice A

7. 7. 8. 9. 10.