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MATH 221

MATH 221. Integrated Learning System Week 3, Lecture 2 Normal Distribution: Finding Probabilities and Values. Comparing Normal Distributions.

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MATH 221

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  1. MATH 221 Integrated Learning System Week 3, Lecture 2 Normal Distribution: Finding Probabilities and Values

  2. Comparing Normal Distributions The Scholastic Aptitude Test (SAT) and the ACT are exams used by colleges to evaluate undergraduate applicants. SAT scores are normally distributed with a mean of 1000 and a standard deviation of 200. ACT scores are normally distributed with a mean of 20 and a standard deviation of 5. Assume a student took both tests and scored 1225 on the SAT and 26 on the ACT. Which is better? How do you know?

  3. Probability and the Normal Distribution The lengths of Atlantic croaker fish are normally distributed with a mean of 10 inches and a standard deviation of 2 inches. You are fishing on a pier on the east coast of the United States and catch a croaker. What is the probability that the croaker is exactly 10 inches long? (Adapted from problem 8, page 222 in Larson and Farber)

  4. Probability and the Normal Distribution

  5. Probability and the Normal Distribution 0.5 0.30854

  6. Standard Normal Probability Table

  7. Using the Table

  8. Using Technology: TI-83 normalpdf(x,,) – Probability density function normalcdf(L,U,,) – Cumulative probability density function

  9. Using Technology: EXCEL

  10. Using Technology: EXCEL

  11. Exercise 1 • In a recent year the ACT scores for high school students with a 3.50 to 4.00 grade point average were normally distributed with a mean of 24.3 and a standard deviation of 4.2. A student who took the ACT is randomly selected. • Find the probability that the student’s ACT score is less than 20. • Find the probability that the student’s ACT score is between 20 and 29. • Find the probability that the student’s ACT score is greater than 29.

  12. Using Technology: TI-83 norminv(p) – inverse standard normal function

  13. Finding Values

  14. Exercise 2 • In a survey of men in the U.S. (ages 20 – 29), the mean height was 69.2 inches with a standard deviation of 2.9 inches. • What height represents the 95th percentile? • What height represents the first quartile?

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