SAT Scores. In May 2018, The College Board reported the following mean scores for two parts of the Scholastic Aptitude Test (SAT): Evidence-Based Reading and Writing 533 Mathematics 527 Assume that the population standard deviation on each part of the test is s = 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 533 on the Evidence-Based Reading and Writing 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 527 on the Mathematics part of the test?

d. What is the standard error of the mean if sample size is 180?

How does this compare to your standard error from parts a and b?Explain why the difference exists.

Better Business Bureau Complaints. In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .80, the same as the overall proportion of complaints settled in 2016.

a. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of p.

b. Based upon a sample of 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?

c. What is the probablity the sample proportion will exceed 0.35? (This part c is different from that found in your textbook.)