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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.
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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?
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College and Drinking 3 8 5 ?
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3 8 5 ? We have to “standardize” it. Change the scores 3, 5, 8 to z-scores. 0
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College and Drinking 3 8 50 0.952 5 0.133 5 0.9525 – 0.1335 = 0.8190 or 81.9% 81.9 %
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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?
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Curfews 45 35 ?
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Curfews 45 35 ? We have to “standardize” it. Change the scores 35 and 45 to z- scores. 0
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Curfews A = ? 0 A =.9236 A = ? 1 – 0.9236 0.0764 7.64%
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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.
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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
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Jeep Prices z = ? 33,100 25% z = - 0.67 z = 0 The bottom 25% will pay $31,760.
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PRACTICE PROBLEMS Pages 310 – 311 #48, 50, 51, 53 Do it on a separate sheet of paper. Show all work and diagrams used.
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