7. Based upon extensive data from a national high school educational testing program, the standard deviation of national test scores for mathematics was found to be 120 points. If a sample of 225 students are given the test, what would be the standard error of the mean?
8. Based upon extensive data from a national high school educational testing program, the standard deviation of national test scores for critical reading was found to be 115 points.
It a sample of 500 students are given the test, what would be the standard error of the mean?
9. Suppose that the mean score for the mathematics test cited in Problem 7 is 610. What is the probability that a random sample of 225 students will have a mean score of more than 625? Less than 600?
10. Suppose that the mean score for the critical reading test cited in Problem 8 is 580. What is the probability that a random sample of 500 students will have a mean score of more than 590? Less than 575?
11. In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.7 mpg. Suppose that the car manufacturer samples five cars from its assembly line and tests them for mileage ratings.
a. What is the distribution of the mean mpg for the sample?
b. What is the probability that the mean mpg of the sample will be greater than
31 mpg?
c. What is the probability that the mean mpg of the sample will be less than 29.5 mpg?
