Chapter 4: Discrete Random Variables
4.9 Using Technology for the Hypergeometric Distribution
Learning Objectives
By the end of this section, the student should be able to:
- use technology to solve problems involving the Hypergeometric Distribution
This is another section to show technology tools that can be used to help with the statistics concepts taught in this chapter. This section will cover tools to help solve problems involving the Hypergeometric Distribution.
Graphing Calculator
Currently, the TI-83+ and TI-84 do not have built-in hypergeometric probability distribution functions. We will have to rely on the additional technology tools to assist as with these problems.
Additional Technology Tools
In addition to the graphing calculator, there are some additional technology tools that can be used for the concepts covered on this page. Below are links to helpful videos for those tools:
- Excel:
Microsoft Excel
You can calculate probabilities in Excel using HYPGEO.DIST(x, n, r, r+b, True/False), where False computes [latex]P(X=x)[/latex], and True computes [latex]P(X \leq x)[/latex]. Let's see some examples from the Section.
Your Turn!
A school site committee is to be chosen randomly from five men and six women. Let [latex]X =[/latex] the number of women on the committee of four. The women are the group of interest (first group). The random variable [latex]X[/latex] takes on the values 0, 1, 2, 3, 4, where [latex]r = 6[/latex], [latex]b = 5[/latex], and [latex]n = 4[/latex], and [latex]X \sim H(6, 5, 4)[/latex]. If the committee consists of four members chosen randomly, what is the probability that two of them are women?
Solution
Using Excel's HypGeom.Dist, [latex]P(X = 2) = \text{HYPGEOM.DIST}(2,4,6,11, \text{FALSE}) \approx 0.4545[/latex]. The probability that there are exactly two women on the committee is about 0.45.
Your Turn!
An intramural basketball team is to be chosen randomly from 15 upperclassmen and 12 underclassmen. The team has ten slots. You want to know the probability that eight of the players will be upperclassmen. What is the group of interest and the sample? Find the probability using a computer.
Solution
The group of interest are the upperclassmen, and the sample is 10. We have [latex]P(X=8)=\text{HYPGEOM.DIST}(8,10,15,27,\text{FALSE}) \approx 0.05[/latex].
Section Practice
Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient.
- In words, define the random variable [latex]X[/latex].
- List the values that [latex]X[/latex] may take on.
- Give the distribution of [latex]X[/latex]. [latex]X \sim \underline{\hspace{2cm}} ( \underline{\hspace{2cm}} , \underline{\hspace{2cm}} )[/latex]
- How many instructors do you expect on the committee who are not technically proficient?
- Find the probability that at least five on the committee are not technically proficient.
- Find the probability that at most three on the committee are not technically proficient.
Solution
- [latex]X =[/latex] the number of people on the committee who are not technically proficient
- [latex]0, 1, 2, 3, 4, 5, 6, 7, 8[/latex]
- [latex]X \sim H(10, 8, 28)[/latex]
- 2.8571
- 0.0772
- 0.7160
