2. 6.5 Applications of the Normal Distribution Objectives: By the end of this section, I will be able to… 1) Compute probabilities for a given value of any normal random variable. 2) Find the appropriate value of any normal random variable, given an area or probability.

3. Bad college students! 1) The mean number of beers a male college student can drink before getting out of control is about 5 with a standard deviation of 1.8. If a college male is selected at random, what is the probability that the student drinks between 3 and 8 beers?

4. College and Drinking 3 8 5 ?

5. 3 8 5 ? We have to “standardize” it. Change the scores 3, 5, 8 to z-scores. 0

6. College and Drinking 3 8 50 0.952 5 0.133 5 0.9525 – 0.1335 = 0.8190 or 81.9% 81.9 %

7. Curfews 2) In a recent study it was found that the number of minutes seniors stay out past curfew is an average of 35 minutes with a standard deviation of 7 minutes. If a senior is selected at random, what is the probability that the senior stayed out for more than 45 minutes?

8. Curfews 45 35 ?

9. Curfews 45 35 ? We have to “standardize” it. Change the scores 35 and 45 to z- scores. 0

10. Curfews A = ? 0 A =.9236 A = ? 1 – 0.9236 0.0764 7.64%

11. Jeep Prices 3) The average price of a 2011 Jeep Wrangler is $33,100 with s = $2,000. Find the price that the bottom 25% of people pay.

12. Jeep Prices z = ? 33,100 25% 0.25 Go to Chart and find closest to A = 0.25 z = -0.67 is A = 0.2514 This one is 0.0014 away z = -0.67 z = 0 z = -0.68 is A = 0.2483 This one is 0.0017 away

13. Jeep Prices z = ? 33,100 25% z = - 0.67 z = 0 The bottom 25% will pay $31,760.

14. PRACTICE PROBLEMS Pages 310 – 311 #48, 50, 51, 53 Do it on a separate sheet of paper. Show all work and diagrams used.