The Random Numbers applet generates a list of n random numbers from 1 to N, where n is the size of the sample and N is the size of the population. The list generated often contains repetitions of one or more numbers.

a. Using the applet Random Numbers, enter 1 for the minimum value, 10 for the maximum value, and 10 for the number of samples. Then click on Sample. Look at the results, and list any numbers that are repeated and the number of times each of these numbers occurs.

b. Repeat part (a), changing the maximum value to 20 and keeping the size of the sample fixed at 10. If you still have repetitions, repeat the process, increasing the maximum value by 10 each time but keeping the size of the sample fixed. What is the smallest maximum value for which you had no repetitions?

c. Describe the relationship between the population size (maximum value) and the number of repetitions in the list of random numbers as the population size increases and the sample size remains the same. What can you conclude about using a random number generator to choose a relatively small sample from a large population?