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5.7 Practice 2: binomial distribution

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This module provides a practice of Binomial Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student learning outcomes

  • The student will construct the Binomial Distribution.

Given

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 pick 8 first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status

Interpret the data

In words, define the random Variable X.

X = the number that reply “yes”

X ~ ___________

B (8,0.713)

What values does the random variable X take on?

0,1,2,3,4,5,6,7,8

Construct the probability distribution function (PDF).

x P(x)

On average ( u ) , how many would you expect to answer yes?

5.7

What is the standard deviation ( σ ) ?

1.28

What is the probability that at most 5 of the freshmen reply “yes”?

0.4151

What is the probability that at least 2 of the freshmen reply “yes”?

0.9990

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

Blank graph with horizontal and vertical axes.

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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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