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Practice 4: Geometric Distribution

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides further practice with topics of Geometric Distribution in Statistics.

Student Learning Outcomes

  • The student will analyze the properties of a geometric distribution.

Given:

Use the information from the Binomial Distribution Practice shown below.

The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. (Source: http://heri.ucla.edu/PDFs/pubs/TFS/Norms/Monographs/TheAmericanFreshman2011.pdf)

Suppose that you randomly select freshman from the study until you find one who replies “yes.” You are interested in the number of freshmen you must ask.

Interpret the Data

Exercise 1

In words, define the Random Variable XX.

Exercise 2

XX ~

Solution

G(0.713)

Exercise 3

What values does the random variable X X take on?

Solution

1,2,…

Exercise 4

Construct the probability distribution function (PDF). Stop at x = 6x=6.

Table 1
xx P(x)P(x)
1  
2  
3  
4  
5  
6  

Exercise 5

On average(μμ), how many freshmen would you expect to have to ask until you found one who replies "yes?"

Solution

1.4

Exercise 6

What is the probability that you will need to ask fewer than 3 freshmen?

Solution

0.9176

Exercise 7

Construct a histogram or plot a line graph. Label the horizontal and vertical axes with words. Include numerical scaling.

Blank graph with vertical and horizontal axes.

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