Chapter 5, Problem 108CRE

Soda A soda-bottling plant has a flaw in that 20% of the bottles it fills do not have enough soda in them. The sodas are sold in six-packs. Follow these steps to carry out a simulation to find the probability that three or more bottles in a six-pack will not have enough soda.

a. Identify the action with a random outcome, and explain how you will simulate this outcome using the random number table in Appendix A. If you want to get the same answers we got, use all the possible one digit numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), and use some at the beginning of the list of numbers to represent bad and the rest to represent good. What numbers would represent bad and what numbers would represent good, and why?

b. Describe how you will simulate a single trial.

c. Describe the event of interest—that is, the event for which you wish to estimate a probability.

d. Carry out 10 trials, beginning with the first digit on line 15 of the random number table in Appendix A. For each trial, list the digits chosen, the outcomes they represent, and whether or not the event of interest occurred.

e. What is the experimental probability that you get three or more “bad” bottles in a six-pack?