# Question: The College Board reported the following mean scores for the

The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009):

Critical Reading ........ 502

Mathematics .......... 515

Writing ............ 494

Assume that the population standard deviation on each part of the test is σ 5 100.

a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).

c. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Comment on the differences between this probability and the values computed in parts (a) and (b).

Critical Reading ........ 502

Mathematics .......... 515

Writing ............ 494

Assume that the population standard deviation on each part of the test is σ 5 100.

a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).

c. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Comment on the differences between this probability and the values computed in parts (a) and (b).

## Answer to relevant Questions

For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return (The Wall Street Journal, October 25, 2012). The mean amount of deductions ...Assume that the population proportion is .55. Compute the standard error of the proportion, σṕ, for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the ...The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.a. Show ...A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x. If test results over a long ...In an attempt to assess total daily travel taxes in various cities, the Global Business Travel Association conducted a study of daily travel taxes on lodging, rental cars, and meals (GBTA Foundation website, October 30, ...Post your question