A researcher wishes to use a random number table to pick between three groups labelled X, Y, and Z.X is to be chosen with a probability of 13/63, Y with a probability of 28/63, and Z with a probability of 22/63.How can the researcher assign random numbers to achieve these probabilities?
A)Assign 1 through 13 to X, 1 through 28 to Y, and 1 through 22 to Z
B)Assign 1 through 13 to X, 14 through 28 to Y, and 14 through 63 to Z
C)Assign 1 through 13 to X, 14 through 41 to Y, and 42 through 100 to Z
D)Assign 1 through 13 to X, 14 through 41 to Y, and 42 through 63 to Z

Question

Quizplus · Accepted Answer

To assign these probabilities, we need to ensure that each group has a range of numbers that corresponds to their respective probabilities. 
X has a probability of 13/63, which means it should have a range of 13 numbers out of 63.
Y has a probability of 28/63, which means it should have a range of 28 numbers out of 63.
Z has a probability of 22/63, which means it should have a range of 22 numbers out of 63.
Using option D, we can assign the numbers 1-13 to X, 14-41 to Y, and 42-63 to Z. This ensures that each group has the correct range of numbers that correspond to their respective probabilities. To assign random numbers that achieve the desired probabilities, we need to allocate ranges of numbers to each group such that the length of the range is proportional to the probability of the group.

In other words, since X has a probability of 13/63, it should be allocated a range that is 13/63 of the total range of numbers. Similarly, Y should be allocated a range of 28/63 and Z should be allocated a range of 22/63.

Based on this reasoning, we can see that choice D is the correct answer:

- Assign 1 through 13 to X: This range has a length of 13.
- Assign 14 through 41 to Y: This range has a length of 28.
- Assign 42 through 63 to Z: This range has a length of 22.

The total length of the ranges is 13+28+22 = 63, which covers all possible random numbers. Furthermore, the length of each range is proportional to the probability of the corresponding group, as desired.

A Researcher Wishes to Use a Random Number Table to Pick