SOCR Courses 2012 2013 Stat13 1 Lab3

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(Problem 5)
(Problem 2)
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==== Problem 2 ====   
==== Problem 2 ====   
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For X Binomial(250; 0.65), use [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html SOCR Distributions] to compute:
+
For X ~ Binomial(250; 0.65), use [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html SOCR Distributions] to compute:
* P(X = 146)
* P(X = 146)
* P(X >=237)
* P(X >=237)

Revision as of 14:36, 22 April 2013

Contents

Stats 13.1 - Laboratory Activity 3

The binomial distribution is a probability distribution which is used to model the probability of obtaining k successes out of n total trials when we have exactly two, disjoint, possible outcomes, trials are independent and the probability of the outcomes is stable/constant.

You can access the applet for any of the SOCR distributions and select the Binomial Distribution calculator.

Binomial Distribution Activity

Problem 1

Suppose X ~ Binomial(10, 0.5) compute by hand:

  • P(X = 7)
  • E(X)
  • SD(X)

Problem 2

For X ~ Binomial(250; 0.65), use SOCR Distributions to compute:

  • P(X = 146)
  • P(X >=237)
  • P(39 < X < 127)

Problem 3

For X ~ Bin(32; 0.81), simplify the equations by hand and then use SOCR to compute.

  • P(X >= 24 \(\cap \) X < 20)
  • P(X >= 24 \(\cup \) X < 20)
  • P(X > 23 \(\cup \) X < 30)

Problem 4

Plot the following distributions and take SNAPSHOTS of those denoted by (*):

Group A
  • X ~ Bin(8; 0.2) (*)
  • X ~ Bin(15; 0.2)
  • X~ Bin(25; 0.2)
  • X~ Bin(55; 0.2)
  • X~ Bin(95; 0.2) (*)
Group B
  • X~ Bin(30; 0.05) (*)
  • X~ Bin(30; 0.2)
  • X~ Bin(30; 0.5) (*)
  • X~ Bin(30; 0.9) (*)
  • X~ Bin(95; 1)

Problem 5

Use your snapshots from question 4 to answer the following questions:

  • Describe how the distribution changes as the number of trials increases.
  • Describe how the distribution changes as the probability of success changes.
  • Write a few 'rules of thumbs' to help you remember the effects of changing n and p.



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