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Essential Questions

Essential Questions. How do we use tables to estimate areas under normal curves? How do we recognize data sets that are not normal?. Example 1: Joint and Marginal Relative Frequencies.

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Essential Questions

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  1. Essential Questions • How do we use tables to estimate areas under normal curves? • How do we recognize data sets that are not normal?

  2. Example 1: Joint and Marginal Relative Frequencies Jamie can drive her car an average of 432 gallons per tank of gas, with a standard deviation of 36 miles. Use the graph to estimate the probability that Jamie will be able to drive more than 450 miles on her next tank of gas. The area under the normal curve is always equal to 1. Each square on the grid has an area of 10(0.001) = 0.01. Count the number of grid squares under the curve for values of x greater than 450. There are about 31 squares under the graph, so the probability is about 31(0.01) = 0.31 that she will be able to drive more than 450 miles on her next tank of gas.

  3. Example 2: Joint and Marginal Relative Frequencies Estimate the probability that Jamie will be able to drive less than 400 miles on her next tank of gas? There are about 19 squares under curve less than 400, so the probability is about 19(0.01) = 0.19 that she will be able to drive less than 400 miles on the next tank of gas.

  4. Example 3: Using Standard Normal Values Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12. a. Estimate the probability that a randomly selected student scored less than 148. The probability of scoring less than 148 is 0.16.

  5. Example 3: Using Standard Normal Values Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12. b. Estimate the probability that a randomly selected student scored between 154 and 184. The probability of scoring between 154 and 184 is 0.67.

  6. Example 4: Using Standard Normal Values Scores on a test are normally distributed with a mean of 142 and a standard deviation of 18. Estimate the probability of scoring above 106. For greater than, use the opposite sign The probability of scoring above 106 is 0.98.

  7. Scores on a test are normally distributed with a mean of 80 and a standard deviation of 5. Use the table below to find each probability. • A randomly selected student scored above 90. • A randomly selected student scored below 75. • A randomly selected student scored between 75 and 85

  8. Lesson 2.3 Practice B

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