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Essential Questions

Thursday, November 4. Essential Questions. How do I use normal distributions in finding probabilities?. 7.4. Use Normal Distributions. A normal distribution with mean x and standard deviation s has these properties:. + s. – s. – 2 s. – 2 s. + 2 s. – 3 s. + 3 s. – 3 s.

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Essential Questions

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  1. Thursday, November 4 Essential Questions • How do I use normal distributions in finding probabilities?

  2. 7.4 Use Normal Distributions A normal distribution with mean x and standard deviation s has these properties: + s – s – 2s – 2s + 2s – 3s + 3s – 3s + 2s – s + s + 3s x x x x x x x x x x x x x Standard Deviation of a Data Set • The total area under the related normal curve is ____. • About ___% of the area lies within 1 standard deviation of the mean. • About ___% of the area lies within 2 standard deviation of the mean. • About _____% of the area lies within 3 standard deviation of the mean. 34% 34% 68% 13.5% 13.5% 95% 2.35% 2.35% 99.7% 0.15% 0.15% x

  3. 7.4 Use Normal Distributions + 3s – 3s + 2s – 2s – s + s x x x x x x x Find a normal probability Example 1 A normal distribution has a mean x and standard deviation s. For a randomly selected x-value from the distribution, find Solution The probability that a randomly selected x-value lies between _______ and _________ is the shaded area under the normal curve. Therefore:

  4. 7.4 Use Normal Distributions • A normal distribution has mean x and standard deviation s. For a randomly selected x-value from the distribution, find – s + s + 3s + 2s – 3s – 2s x x x x x x x Checkpoint. Complete the following exercise.

  5. 7.4 Use Normal Distributions Interpret normally distributed data Example 2 The math scores of an exam for the state of Georgia are normally distributed with a mean of 496 and a standard deviation of 109. About what percent of the test-takers received scores between 387 and 605? 605 714 169 278 387 496 823 Solution The scores of 387 and 605 represent ____ standard deviation on either side of the mean. So the percent of test-takers with scores between 387 and 605 is

  6. 7.4 Use Normal Distributions Checkpoint. Complete the following exercise. • In Example 2, what percent of the test-takers received scores between 496 and 714? 34% 13.5% 605 714 169 278 387 496 823

  7. 7.4 Use Normal Distributions Use a z-score and the standard normal table Example 3 In Example 2, find the probability that a randomly selected test-taker received a math score of at most 630? Solution Sep 1 Find the z-score corresponding to an x-value of 630.

  8. 7.4 Use Normal Distributions Use a z-score and the standard normal table Example 3 In Example 2, find the probability that a randomly selected test-taker received a math score of at most 630? Solution Sep 2 Use the standard normal table to find The table shows that P(z< ____) = _______. So, the probability that a randomly selected test-taker received a math score of at most 630 is about ________.

  9. 7.4 Use Normal Distributions Checkpoint. Complete the following exercise. • In Example 3, find the probability that a randomly selected test-taker received a math score of at most 620?

  10. 7.4 Use Normal Distributions Pg. 277, 7.4 #1-21

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