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Math 5389 Final Use the following to answer questions 1-3: The scores of individual students on the American College Testing (ACT) Program Composite

What is variance,
2
x σ , of the sampling distribution of the sample mean x ?

Page 1 Math 5389 Final Use the following to answer questions 1-3: The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. 1. What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students? A) 1.0 B) 3.1 C) 6.0 D) 18.6 2. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students? A) 1.0 B) 3.1 C) 6.0 D) 18.6 3. What is the sampling distribution of the sample mean score for a random sample of 36 students? A) Approximately Normal, but the approximation is poor. B) Approximately Normal, and the approximation is good. C) Exactly Normal. D) Neither Normal nor nonNormal. It depends on the particular 36 students selected. Use the following to answer questions 4-5: Chocolate bars produced by a certain machine are labeled 8.0 oz. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 oz and a standard deviation of 0.1 oz. 4. A quality control manager initially plans to take a simple random sample of size n from the production line. If he were to double his sample size (to 2 n ), by what factor would the standard deviation of the sampling distribution of X change? A) 1 2 B) 12 C) 2 D) 2
Page 2 5. If the quality control manager takes a simple random sample of ten chocolate bars from the production line, what is the probability that the sample mean weight of the ten sampled chocolate bars will be less than 8.0 oz? A) 0 B) 0.00078 C) 0.0316 D) 0.1587 Use the following to answer questions 6-7: The weights of medium oranges packaged by an orchard are Normally distributed with a mean of 14 oz and a standard deviation of 2 oz. 6. Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the sample mean weight of a random sample of ten medium oranges? (i.e., N (mean, standard error) A) N (14, 2) B) N (14, 0.63) C) N (14, 0.2) D) N (1.4, 0.2) 7. Ten medium oranges will be randomly selected from a package. What is the probability that the mean weight of the ten oranges will be more than 15? Use the following to answer questions 8-10: The length of time it takes to get through the security checks at a very large urban airport is a random variable with mean μ = 20.6 minutes and standard deviation σ = 8.4 minutes. A simple random sample of 36 airline passengers is to be observed going through security. 8. What is the mean, x μ , of the sampling distribution of the sample mean x ? A) 8.4 minutes B) 20.6 minutes C) 1.4 minute D) Close to 20.6 minutes but we can't be certain without having the data to determine it. E) Without knowing the distribution we don't know what it will be.
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