Recall our earlier scenario: The Federal Pell ased 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 2 30. (Click to view hint) 2. What theorem states that we can use the normal approximation? The central 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. MY = x (Click to view hint) OF = * (Round to the nearest tenth.) (Click to view hint) b. The z-score for 2940 is x . (Click to view hint) The annual salary for a certain job has a normal distribution with a mean of $54, 000 and a standard deviation of o = $5000. 1. Which sample size would allow us to use the normal approximation? n = all can be used . (Click to view hint) 2. What is the probability that the mean salary of random sample of 100 workers is no more than $54, 215? a. My = 54000 (Do not include the dollar sign) b. Ox = x (Click to view hint) d. P(x s * v 54, 215) = P(z s . x )= e. There is a(n) * % chance that the mean size of a random sample is no more than $54, 215. 3. The annual salary for a certain job has a normal distribution with a mean of $54, 000 and a standard deviation of o = $5000. What is the probability that the mean salary of random sample of 100 workers is more than $49, 000? b. P(x > * 49000) = P(z > )= c. There is a(n) * % chance that the mean salary of a random sample is more than $49, 000. 4. The annual salary for a certain job has a normal distribution with a mean of $54, 000 and a standard deviation of o = $5000. What is the probability that the mean salary of a random selected sample has between $49, 000 and $56, 150? b. P(49000