sat suite question viewer

Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Medium

A store manager reviewed the receipts from 80 customers who were selected at random from all the customers who made purchases last Thursday. Of those selected, 20 receipts showed that the customer had purchased fruit. If 1,500 customers made purchases last Thursday, which of the following is the most appropriate conclusion?

Exactly 75 customers must have purchased fruit last Thursday.

Exactly 375 customers must have purchased fruit last Thursday.

The best estimate for the number of customers who purchased fruit last Thursday is 75.

The best estimate for the number of customers who purchased fruit last Thursday is 375.

Back question 17 of 25 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Explanation

Choice D is correct. It’s given that the manager took a random selection of the receipts of 80 customers from a total of 1,500. It’s also given that of those 80 receipts, 20 showed that the customer had purchased fruit. This means that an appropriate estimate of the fraction of customers who purchased fruit is $the fraction 20 over 80$ , or $one fourth$ . Multiplying this fraction by the total number of customers yields $one fourth times 1,500, equals 375$ . Therefore, the best estimate for the number of customers who purchased fruit is 375.

Choices A and B are incorrect because an exact number of customers can’t be known from taking a random selection. Additionally, choice A may also be the result of a calculation error. Choice C is incorrect and may result from a calculation error.