Question

A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even​ number, you get a 10​% discount on your purchase that day. If the card is an odd number greater than​ 6, you get a 40​% discount.​ Otherwise, you get a ​25% discount. The table shows the results of 500 customers. What is the relative frequency for each​ discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the ​25% ​discount, does this seem like an appropriate​ method? Explain.

Answer 1

Answer: We can use the data given in the table to calculate the relative frequency of each discount as follows:

- For a 10% discount: 160 customers received even-numbered cards, so the relative frequency is 160/500 = 0.32, or 32%.

- For a 25% discount: 222 customers received odd-numbered cards less than or equal to 6, so the relative frequency is 222/500 = 0.444, or 44.4%.

- For a 40% discount: 118 customers received odd-numbered cards greater than 6, so the relative frequency is 118/500 = 0.236, or 23.6%.

Regarding the question about whether this method will lead to approximately half of the customers receiving a 25% discount, we can see that the relative frequency for a 25% discount is actually higher than the desired 50%. Therefore, this method is not appropriate if the manager wants approximately half of the customers to receive a 25% discount.

To achieve this, the store can change the rule to offer a 25% discount for odd-numbered cards less than or equal to 5 and a 50% discount for odd-numbered cards greater than 5. This will result in the relative frequency for a 25% discount to be close to 50%.

Explanation: