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Chapter 8 Extension

Chapter 8 Extension. Normal Distributions. Objectives. Recognize normally distributed data Use the characteristics of the normal distribution to solve problems. Normal Distribution. Standardized test results, like those used for college admission, follow a normal distribution

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Chapter 8 Extension

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  1. Chapter 8 Extension Normal Distributions

  2. Objectives • Recognize normally distributed data • Use the characteristics of the normal distribution to solve problems

  3. Normal Distribution • Standardized test results, like those used for college admission, follow a normal distribution • Probability distributions can be based on either discrete or continuous data. Usually discrete data result from counting and continuous data result from measurement

  4. Normal Distribution • The binomial distribution were discrete probability distributions because there was a finite number of possible outcomes. The graph shows the probability distribution of the number of questions answered correctly when guessing on a true-false test.

  5. Normal Distribution • In a continuous probability distribution, the outcome can be any real number – for example, the time it takes to complete at task • You may be familiar with the bell-shaped curve called the normal curve. A normal distribution is a function of the mean and standard deviation of a data set that assigns probabilities to intervals of real numbers associated with continuous random variables

  6. Normal Distributions • The probability assigned to a real-number interval is the area under the normal curve in that interval. Because the area under the curve represents probability, the total area under the curve is 1 • The maximum value of a normal curve occurs at the mean • The normal curve is symmetric about a vertical line through the mean • The normal curve has a horizontal asymptote at y = 0

  7. Normal Distributions The figure shows the percent of data in a normal distribution that falls within a number of standard deviations from the mean Addition shows the following: • About 68% of the data lies within 1 standard deviation of the mean • About 95% of the data lie within 2 standard deviations of the mean • Close to 99.8% of the data lie within 3 standard deviations of the mean

  8. Example • The SAT is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. What percent of SAT scores are between 300 and 500?

  9. Example (Continued) • What is the probability that an SAT score is below 700?

  10. Example (Continued) • What is the probability that an SAT score is less than 400 or greater than 600? • What is the probability that an SAT score is above 300?

  11. Homework • Page 595 #1-8

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