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Now that we know when we can use the normal distribution, we can use the Empirical Rule and the Normal Table (opens in new window) to find the probabilities. Example 1 Recall our earlier scenario: The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain post-baccalaureat students to promote access to post-secondary education. According to the National Post-secondary Student Aid Study conducted by the U. S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2, 600. Assume that the standard deviation in Pell grants award was $500. If we randomly sample 36 Pell grant recipients, would you be surprised if the mean grant amount for the sample was $2, 940? 1. Can we use use the normal approximation? • (Click to view hint) 2. What theorem states that we can use the normal approximation? The Limit Theorem 3. If the population mean is 2600, how can we determine if 2940 is unusual? a. If 2940 is unusual it will be beyond • standard deviations of the mean. = Ed (Click to view hint) (Round to the nearest tenth.) (Click to view hint) b. The z-score for 2940 is (Click to view hint) c. $2940 an unusual award. Check

Now that we know when we can use the normal distribution, we can use the Empirical Rule and the Normal Table (opens in new window) to find the probabilities. Example 1 Recall our earlier scenario: The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain post-baccalaureat students to promote access to post-secondary education. According to the National Post-secondary Student Aid Study conducted by the U. S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2, 600. Assume that the standard deviation in Pell grants award was $500. If we randomly sample 36 Pell grant recipients, would you be surprised if the mean grant amount for the sample was $2, 940? 1. Can we use use the normal approximation? • (Click to view hint) 2. What theorem states that we can use the normal approximation? The Limit Theorem 3. If the population mean is 2600, how can we determine if 2940 is unusual? a. If 2940 is unusual it will be beyond • standard deviations of the mean. = Ed (Click to view hint) (Round to the nearest tenth.) (Click to view hint) b. The z-score for 2940 is (Click to view hint) c. $2940 an unusual award. Check

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Probabilities: Sampling Means ing: Now that we know when we can use the normal distribution, we can use the Empirical Rule and the Normal Table (opens in new window) to find the probabilities. Example 1 Recall our earlier scenario: The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain post-baccalaureate students to promote access to post-secondary education. According to the National Post-secondary Student Aid Study conducted by the U. S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2, 600. Assume that the standard deviation in Pell grants awards was $500. If we randomly sample 36 Pell grant recipients, would you be surprised if the mean grant amount for the sample was $2, 940? 1. Can we use use the normal approximation? + (Click to view hint) 2. What theorem states that we can use the normal approximation? The Limit Theorem 3. If the population mean is 2600, how can we determine if 2940 is unusual? a. If 2940 is unusual it will be beyond : standard deviations of the mean. (Click to view hint) = 20 (Round to the nearest tenth.) (Click to view hint) b. The z-score for 2940 is (Click to view hint) c. $2940 an unusual award. Check
Transcribed Image Text:Probabilities: Sampling Means ing: Now that we know when we can use the normal distribution, we can use the Empirical Rule and the Normal Table (opens in new window) to find the probabilities. Example 1 Recall our earlier scenario: The Federal Pell Grant Program provides need-based grants to low-income undergraduate and certain post-baccalaureate students to promote access to post-secondary education. According to the National Post-secondary Student Aid Study conducted by the U. S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2, 600. Assume that the standard deviation in Pell grants awards was $500. If we randomly sample 36 Pell grant recipients, would you be surprised if the mean grant amount for the sample was $2, 940? 1. Can we use use the normal approximation? + (Click to view hint) 2. What theorem states that we can use the normal approximation? The Limit Theorem 3. If the population mean is 2600, how can we determine if 2940 is unusual? a. If 2940 is unusual it will be beyond : standard deviations of the mean. (Click to view hint) = 20 (Round to the nearest tenth.) (Click to view hint) b. The z-score for 2940 is (Click to view hint) c. $2940 an unusual award. Check
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