SAT Math Multiple Choice Question 189: Answer and Explanation

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Question: 189

9. A survey was conducted among a randomly chosen sample of full-time salaried workers about satisfaction in their current jobs. The table below shows a summary of the survey results.

Reported Job Satisfaction by Education Level (in thousands)

Of the people whose highest level of education was a bachelor's degree who reported job satisfaction, 1,000 people were randomly selected to complete a follow-up survey in which they were asked about their salary satisfaction. There were 658 people in this follow-up sample who said that they were satisfied with their salaries, and the other 342 people were not satisfied. Using the data from both the initial survey and the follow-up survey, which of the following statements is most likely true?

  • A. Approximately 16 million people with bachelor's degrees would report salary satisfaction.
  • B. Approximately 24 million people with bachelor's degrees would report salary satisfaction.
  • C. Approximately 47 million people with bachelor's degrees would report salary satisfaction.
  • D. Approximately 72 million people with bachelor's degrees would report salary satisfaction.

Correct Answer: A

Explanation:

A All of the answer choices refer to the number of salary-satisfied bachelor's-degree-holders, so you must use the follow-up survey results to calculate that number. First, find the percent of bachelor's-degree-holders who reported also being salary-satisfied in the follow-up survey. This number was 658 out of the 1,000 people, so divide 658 by 1,000 and then multiply by 100 to get the percent. The result is 65.8% salary-satisfied bachelor's-degree-holders for the follow-up survey. Since the people in the follow-up were randomly selected, you can assume that they are generally representative of the bachelor's-degree-holding population at large. Therefore, the 65.8% of salary-satisfied individuals should be true of all 24,236,000 job-satisfied bachelor's-degree-holders. Watch the units on charts-this one is in the thousands, so there are 24,236,000 not 24,236 job-satisfied bachelor's-degree-holders. Multiply 65.8%, or .658, by the total number of bachelor's-degree-holders, 24,236,000, to find that there should be 15,947,288 salary-satisfied, job-satisfied bachelor's-degree-holders. Choice (A) is the closest to this and is the credited response.

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