The binomial tables used by the author are based on a cumulative distribution. Given a sample size (n) and an overall probability of success (p), you can solve probability problems for the binomial distribution using the tables. It is important to learn to use the tables because they help solve some problems much faster than using the binomial formula, which may require many calculations. The key to understanding the tables is that the table is based on a cumulative distribution. Sometimes you need to perform addition and subtraction to get the correct answer. Answer the following questions using the Binomial Table for n = 25 and p = 0.4.
- Solve the probability for x = 8 using the binomial formula.
- Next, get the same answer from the binomial tables. To use the table you have to subtract the cumulative probability for x = 7 from the cumulative probability for x = 8. This leaves the exact probability of 8. Confirm that the table calculation equals the formula calculation (to at least four decimal places).
- What is the probability of more than 8, P(x > 8)? To solve this, you need to subtract the table value for 8 from 1.0000.
- What is the probability of 4 or less, P(x < 5)?
- What is the probability of between 6 and 9, P(x > 5 and x < 10)?