Practice problems for these concepts can be found at:

- Discrete Random Variables Solved Problems for Beginning Statistics
- Discrete Random Variables Supplementary Problems for Beginning Statistics

**EXAMPLE 5.16** If X represents the number of girls in families having four children, then X is a binomial random variable with n = 4 and p = .5. Using formula (*5*.*7*), the distribution of X is determined as follows:

Table 5.9 contains a portion of the table of binomial probabilities found in Appendix 1. The numbers in bold print indicates the portion of the table from which the binomial probability distribution for X is obtained. The probabilities given are the same ones obtained by using formula (*5*.*7*).

**EXAMPLE 5.17** Eighty percent of the residents in a large city feel that the government should allow more than one company to provide local telephone service. Using the table of binomial probabilities, the probability that at least five in a sample of ten residents feel that the government should allow more than one company to provide local telephone service is found as follows. The event "at least five" means five or more and is equivalent to X = 5 or X = 6 or X = 7 or X = 8 or X = 9 or X = 10. The probabilities are added because of the addition law for mutually exclusive events.

- P(X ≥ 5) = P(5) + P(6) + P(7) + P(8) + P(9) + P(10)

- P(X ≥ 5) = .0264 + .0881 + .2013 + .3020 + .2684 + .1074 = .9936

Statistical software is used to perform binomial probability computations and to some extent has rendered binomial probability tables obsolete. Minitab contains routines for computing binomial probabilities. Example 5.18 illustrates how to use Minitab to compute the probability for a single value or the total distribution for a binomial random variable.

**EXAMPLE 5.18** The following output is generated by MINITAB and shows the binomial probability computations given in Example 5.16. The dialog box for the binomial distribution is produced by the pulldown sequence **Calc** **Probability Distribution** **Binomial**. Choose probability, number of trials equal to 4, and p = 0.5. Put the numbers 0 through 4 in column 1 and have the software store the results in C2. The following output is produced in the worksheet.

Practice problems for these concepts can be found at:

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