Chapter 5.2, Problem 27P

Binomial Distribution Table: Symmetry Study the binomial distribution table (Table 3, Appendix II). Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let’s look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.

1. (a) Compare P(3 successes), where p = 0.30, with P(2 successes), where p = 0.70.
2. (b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.
3. (c) Find the value of P(4 successes), where p = 0.30. For what value of r is P(r successes) the same using p = 0.70?
4. (d) What column is symmetric with the one headed by p = 0.20?