PSAT Math Multiple-Choice Question 399: Answer and Explanation

Question: 399

SoFast Internet is hoping to expand its services to three new counties in rural Virginia. According to its research, a total of approximately 86,400 homes in the three counties currently have Internet service. SoFast surveys a sample of 500 randomly selected households with Internet service and finds that 225 are not satisfied with their current provider. SoFast would be the only other Internet service provider in the area, and it is confident that it will be able to acquire 80% of the dissatisfied households. Based on this information and the results of the sample survey, about how many new customers should SoFast be able to acquire?

• A. 31,104
• B. 38,880
• C. 41,608
• D. 69,120

Correct Answer: A

Explanation:

A

Difficulty: Hard

Getting to the Answer: The sample of households was randomly selected, so if (or 45%) of the surveyed households are not satisfied with their current providers, you can infer that 45% of the total households in the three counties are not satisfied with their providers. Multiply by the total number of customers in the population to find that 86,400 × 0.45 = 38,880 customers are not satisfied. Be careful—this is not the correct answer, so don't choose (B). The company is confident that it can acquire 80% of these customers, or 38,880 × 0.80 = 31,104 customers. Choice (A) is correct.