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# 6.5 Applications of the Normal Distribution

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

2. 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?

3. College and Drinking P(drinking between 3 and 8) = ? ? 5 3 8

4. College and Drinking P(drinking between 3 and 8) = ? We have to “standardize” it. Change the scores 3, 5, 8 to z-scores. ? Since 5 = it has a z-score of 0. 5 0 3 8

5. College and Drinking P(drinking between 3 and 8) = ? 81.9% 0.9525 – 0.1335 = 0.8190 or 81.9% 0.9525 0.1335 5 0 3 8

6. 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?

7. Curfews P(>45 minutes) = ? ? 35 45

8. Curfews P(>45 minutes) = ? We have to “standardize” it. Change the scores 35 and 45 to z-scores. ? Since 35 = it has a z-score of 0. 35 0 45

9. Curfews P(>45 minutes) = ? 7.64% 1 – 0.9236 0.0764 A = ? A = ? A = .9236 0

10. 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.

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

12. Jeep Prices P(?) = bottom 25% The bottom 25% will pay \$31,760. z = -0.67, so -0.67 -1,340 25% \$31,760 33,100 z = 0 z = ? z = -0.67

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