Question

Challenge. 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 15% discount on your purchase that day. If the card is an odd number greater than 6, you get a 30% discount. Otherwise, you get a 20% discount. The table shows the results of 400 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 20% discount, does this seem like an appropriate method? Explain.DISCOUNTSCard number/frequency= 1/48, 2/46, 3/46, 4/34, 5/33, 6/42, 7/34, 8/35, 9/39, 10,43What is the relative frequency for a 15% discount? SIMPLIFY

Answer 1

From the data given, we want to construct a frequency distribution table.

The store gives out cards labelled 1 through 10, and the frequency of each card is shown below;

`\begin{gathered} CARD|FREQUENCY|RELATIVE\text{ FREQUENCY} \\ 1|48|0.12 \\ 2|46|0.115 \\ 3|46|0.115 \\ 4|34|0.085 \\ 5|33|0.0825 \\ 6|42|0.105 \\ 7|34|0.085 \\ 8|35|0.0875 \\ 9|39|0.0975 \\ 10|43|0.1075 \\ TOTAL|400|1.00 \end{gathered}`

We now have the relative frequency distribution table (as shown above).

From the details provided in the question,

If the card is an even number, the customer gets a 15% discount for that day.

If the card is an odd number greater than 6, the customer gets a 30% discount.

If the card does not fall into any of the above categories, the customer gets a 20% discount.

(a) Therefore, the relative frequency for a 15% discount would be the addition of the relative frequencies of all even numbered cards. This is shown below;

`\begin{gathered} 2|46|0.115 \\ 4|34|0.085 \\ 6|42|0.105 \\ 8|35|0.0875 \\ 10|43|0.1075 \\ \text{TOTAL}|200|0.50 \end{gathered}`

The relative frequency for 15% discount customers is 0.50

(b) The relative frequency for odd numbers greater than 6 would be the addition of all relative frequencies labeled 7 and 9. This is shown below;