# 4.12 Practice 4: geometric distribution

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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

In words, define the Random Variable $X$ .

$X$ ~

G(0.713)

What values does the random variable $X$ take on?

1,2,…

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

$x$ $\text{P(x)}$
1
2
3
4
5
6

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

1.4

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

0.9176

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

#### Questions & Answers

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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.