Question

Probabilities: Sampling Means 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? Yes, n = 30. . (Click to view hint) 2. What theorem states that we can use the normal approximation? The 76 * 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 3: standard deviations of the mean. * (Click to view hint) * (Round to the nearest tenth.) (Click to view hint) b. The 2-score for 2940 is 68 *. (Click to view hint) Hity 0 = 45 c. $2940 an unusual award. MacBook Air 80 OOO F4 FS PT $ 4 % 5 & 7 6 8

Answer 1

2. The Central Limit Theorem

3.a.

Mu i = 2600

Sigma i = 500 / √36 = 83.33

b.

Z = (x- Mu) / sigma

Z = ( 2940 - 2600) / 500

Z = 0.68

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