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Math III Accelerated

Math III Accelerated. Chapter 11 Data Analysis and Statistics. Warm Up 11.3. Simplify each expression. Round the answer to the nearest hundredth. 11.3 Use Normal Distributions. Objective: Study normal distributions. Vocabulary. Normal Distribution

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Math III Accelerated

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  1. Math III Accelerated Chapter 11 Data Analysis and Statistics

  2. Warm Up 11.3 • Simplify each expression. Round the answer to the nearest hundredth.

  3. 11.3 Use Normal Distributions • Objective: • Study normal distributions.

  4. Vocabulary • Normal Distribution A probability distribution modeled by a bell shaped curve that is symmetric about the mean. • Normal Curve The bell shaped curve that models a normal distribution. • Standard Normal Distribution The normal distribution with mean = 0 and standard deviation = 1.

  5. Properties of the Normal Distribution • Bell-shaped curve with the highest point over the mean. • The curve is symmetric about the mean. • The curve approaches the horizontal axis but never touches or crosses it. • Total area under the curve = 1.

  6. Area Under A Normal Curve • Approximately 68% of the data values lie within one standard deviation of the mean.

  7. Area Under A Normal Curve • Approximately 95% of the data values lie within two standard deviations of the mean.

  8. Area Under A Normal Curve • Almost all (approximately 99.7%) of the data values will be within three standard deviations of the mean.

  9. Example 1 • A normal distribution has mean and standard deviation σ. For a randomly selected x-value from the distribution, find the probability that the x-value lies between and + 3σ.

  10. Checkpoint 1 • A normal distribution has mean and standard deviation σ. For a randomly selected x-value from the distribution, find the probability that the x-value lies between and – σ.

  11. Example 2 • The math scores of the 2004 SAT exam are normally distributed with a mean of 518 and a standard deviation of 114. • About what percent of the test-takers have scores between 518 and 746? • About what percent of the test-takers have scores less than 404?

  12. Checkpoint 2 • The math scores of the 2004 SAT exam are normally distributed with a mean of 518 and a standard deviation of 114. About what percent of the test-takers have scores between 404 and 632?

  13. Example 3 • The blood cholesterol readings for a group of women are normally distributed with a mean of 172 mg/dl and a standard deviation of 14 mg/dl. • About what percent of the women have readings between 158 and 186? • Readings higher than 200 are considered undesirable. About what percent of the readings are undesirable?

  14. Homework 11.3 • Practice 11.3

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