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Discrete Random Variables: Practice 2: Binomial Distribution

Module by: Susan Dean, Dr. Barbara Illowsky

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 practice constructing Binomial Distributions.

Given

The Higher Education Research Institute at UCLA surveyed more than 263,000 incoming freshmen from 385 colleges. 36.7% of first-generation college students expected to work fulltime while in college. (Source: Eric Hoover, The Chronicle of Higher Education, 2/3/2006). Suppose that you randomly pick 8 college freshmen from the survey. You are interested in the number that expect to work full-time while in college.

Interpret the Data

Exercise 1

In words, define the random Variable X.

Solution 1

X X= the number that expect to work full-time.

Exercise 2

X X~______________________

Solution 2

B (8,0.367) B(8,0.367)

Exercise 3

What values does X X take on?

Solution 3

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

Exercise 4

Construct the probability distribution function (PDF) for X X.

XX P(X=x)P(X=x)
   
   
   
   
   
   
   
   
   

Exercise 5

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

Solution 5

2.94

Exercise 6

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

Solution 6

1.36

Exercise 7

What is the probability what at most 5 of the freshmen expect to work full-time?

Solution 7

0.9677

Exercise 8

What is the probability that at least 2 of the freshmen expect to work full-time?

Solution 8

0.8547

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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