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Applications of the Normal Distribution

Applications of the Normal Distribution. Standardizing a Normal Random Variable. The random variable Z is said to have the standard normal distribution with μ = 0, σ = 1. Tables. 1. Determine the area under the standard normal curve that lies to the left of: -2.92.

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Applications of the Normal Distribution

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  1. Applications of the Normal Distribution

  2. Standardizing a Normal Random Variable The random variable Z is said to have the standard normal distribution with μ = 0, σ = 1

  3. Tables

  4. 1. Determine the area under the standard normal curve that lies to the left of: -2.92

  5. 2. Determine the area under the standard normal curve that lies to the right of: 0.53

  6. 3. Determine the area under the standard normal curve that lies between 0.31 and 0.84

  7. 4. Determine the area under the standard normal curve that lies to the left of -3.32 or to the right of 0.24

  8. 5. Find the z-score such that the area under the standard normal curve to the left is 0.7

  9. 6. Find the z-score such that the area under the standard normal curve to the right is 0.4

  10. 7. Find the z-scores that separate the middle 90% of the distribution from the area in the tails of the standard normal distribution

  11. 7. Find the z-scores that separate the middle 90% of the distribution from the area in the tails of the standard normal distribution (cont.)

  12. 8. Assume that the random variable X is normally distributed with mean = 30 and standard deviation = 5. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.P(X > 42)

  13. 9. Assume that the random variable X is normally distributed with mean = 30 and standard deviation = 5. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.P(X < 25)

  14. 10. Assume that the random variable X is normally distributed with mean = 30 and standard deviation = 5. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.P(20 < X < 40)

  15. 11. Assume that the random variable X is normally distributed with mean = 30 and standard deviation = 5. Find each indicated percentile for XThe 15th percentile

  16. Normal Dist: TI-83/84 Functions • Find the probability, percentage, proportion, or area normalcdf(lowerbound,upperbound,μ,σ) • Find the value invnorm(probability, μ,σ) probability is always area to left remember: area = probability

  17. 12. Test Scores Test score are normally distributed with a mean of 65 and a standard deviation of 5: • What is the probability of picking a test score out and getting one less than 70 • What is the probability of picking a test score out and getting one more than 60 • What is the probability of picking a test score out and getting one between 60 and 80

  18. 13. Ages Ages of Cowley students are normally distributed with a mean of 20 and a standard deviation of 5: • What is the probability of picking a student and getting one older than 25 • What is the probability of picking a student and getting one younger than 16 • What is the probability of picking a student and getting one between 18 and 20

  19. 14. Test Scores Test score are normally distributed with a mean of 65 and a standard deviation of 5: • What is the score that separates the top 10% of the class from the rest? • What are the scores that separates the middle 95% of the class from the rest?

  20. Note: • If you get a certain % that you discard and it asks you how many you need to start making to end up with 5000 after the discards (for example) total = (start qty) – (start qty)(discard %) lets say discard % is 0.05 and we want 5000 then: 5000 = s – s(0.05) 5000 = 0.95s 5264 = s

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