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Practice 2: Binomial Distribution

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

Summary: 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

Exercise 1

In words, define the random Variable X.

Solution

X X= the number that reply “yes”

Exercise 2

X X~______________________

Solution

B (8,0.713) B(8,0.713)

Exercise 3

What values does the random variable X X take on?

Solution

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

Exercise 4

Construct the probability distribution function (PDF).

Table 1
xx P(x)P(x)
   
   
   
   
   
   
   
   
   

Exercise 5

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

Solution

5.7

Exercise 6

What is the standard deviation ( σ ) (σ) ?

Solution

1.28

Exercise 7

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

Solution

0.4151

Exercise 8

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

Solution

0.9990

Exercise 9

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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