A store manager finds that his store’s sales are split among four areas – 40% clothing, 40% footwear, 10% housewares, and 10% athletic gear. He wants to run a simulation of the store’s sales using a random digit table.

Which values should be used in this simulation?

A) Use 0 and 1 for clothing, 2 and 3 for footwear, 4 and 5 for housewares, and 6 and 7 for athletic gear. Use a random digit table to generate one-digit numbers, ignoring 8’s and 9’s.
B) Use 0, 1, 2, and 3 for clothing, 4, 5, 6, and 7 for footwear, 8 for housewares, and 9 for athletic gear. Use a random digit table to generate one-digit numbers.
C) Use 40 for clothing, 40 for footwear, 10 for housewares, and 10 for athletic gear. Use a random digit table to generate two-digit numbers, ignoring any besides 40 and 10.
D) Use 1 for clothing, 2 for footwear, 3 for housewares, and 4 for athletic gear. Use a random digit table to generate one-digit numbers, ignoring numbers 5-9.

1 answer

To determine the appropriate values for simulating the store's sales based on the given percentages, we need to assign a range of random digit outcomes that accurately reflects the sales distribution.

The store's sales distribution is as follows:

  • Clothing: 40%
  • Footwear: 40%
  • Housewares: 10%
  • Athletic gear: 10%

To create a simulation using a random digit table, we can assign each category a range of digits that corresponds to its percentage of sales.

First, let's convert the percentages into portions of 100:

  • Clothing: 0-39 (40 digits)
  • Footwear: 40-79 (40 digits)
  • Housewares: 80-89 (10 digits)
  • Athletic gear: 90-99 (10 digits)

Now we can check the options:

A) Use 0 and 1 for clothing, 2 and 3 for footwear, 4 and 5 for housewares, and 6 and 7 for athletic gear. This does not distribute the digits proportionately and only covers a subset of the necessary outcomes (it ignores a lot of digits).

B) Use 0, 1, 2, and 3 for clothing, 4, 5, 6, and 7 for footwear, 8 for housewares, and 9 for athletic gear. Here, clothing and footwear are assigned a proportionate amount, but housewares and athletic gear are not correctly represented by just a single digit each, which does not reflect their 10%.

C) Use 40 for clothing, 40 for footwear, 10 for housewares, and 10 for athletic gear. Use a random digit table to generate two-digit numbers, ignoring any besides 40 and 10. This option suggests generating two-digit numbers but does not cover the entire possible range for 100% sales distribution adequately.

D) Use 1 for clothing, 2 for footwear, 3 for housewares, and 4 for athletic gear. Use a random digit table to generate one-digit numbers, ignoring numbers 5-9. This option does not properly reflect the percentages and does not distribute the valid digits proportionately.

From this analysis, option B appears the closest to creating a proportional representation, but it also needs to distribute digits correctly, especially regarding the smaller percentages. Therefore, none of the provided options fully encapsulate the correct distribution for a simulation based on the stated percentages accurately.

However, if forced to choose one of the available options, B could be used but with the understanding of the limitations concerning the representation of percentages. Ideally, a better approach would have digits ranging per segments as previously outlined.