5.68 Use the Probability applet. The Probability applet simulates tosses of a coin. You can choose the number of tosses n and the probability p of a head. You can therefore use the applet to simulate binomial random variables.

The count of misclassified sales records in Example 5.21 has the binomial distribution with n = 15 and p = 0.08. Set these values for the number of tosses and probability of heads in the applet. Table C shows that the probability of getting a sample with exactly 0 misclassified records is 0.2863. This is the long-run proportion of samples with no bad records. Click “Toss” and “Reset” repeatedly to simulate 25 samples of 15 tosses. Record the number of bad records (the count of heads) in each of the 25 samples.

1. (a) What proportion of the 25 samples had exactly 0 bad records? Do you think this sample proportion is close to the probability?

2. (b) Remember that this probability of 0.2863 tells us only what happens in the long run. Here we’re considering only 25 samples. If X is the number of samples out of 25 with exactly 0 misclassified records, what is the distribution of X?

3. (c) Explain how to use the distribution in part (b) to describe the sampling distribution of in part (a).