SOCR Courses 2012 2013 Stat13 1 Lab3

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== [[SOCR_Courses_2012_2013_Stat13_1 | Stats 13.1]] - Laboratory Activity 3==
== [[SOCR_Courses_2012_2013_Stat13_1 | Stats 13.1]] - Laboratory Activity 3==
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You can access the applet for any of the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SOCR distributions]. Use SOCR to graph the following distributions and answer the questions below.
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The [[AP_Statistics_Curriculum_2007_Distrib_Binomial#Binomial_Random_Variables|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.
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You can access the applet for any of the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SOCR distributions] and select the [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial Distribution calculator].
===[http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial Distribution] Activity ===
===[http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial Distribution] Activity ===
==== Problem 1 ====   
==== Problem 1 ====   
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* X ~ Binom(10, .5)
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Suppose X ~ Binomial(10, 0.5) compute by hand:
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* Find: P(X = 3), E(X), sd(X) from the SOCR output, and verify them with the formulas discussed in class.
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* P(X = 7)
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* E(X)
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* SD(X)
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==== Problem 2 ====  
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==== Problem 2 ====
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* X ~ Binom(10, .1)
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For X � Binomial(250; 0.65), use [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html SOCR Distributions] to compute:
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* Find P(1 ≤ X ≤ 3) from SOCR, and verify using the binomial formula.
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* P(X = 146)
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* P(X >=237)
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* P(39 < X < 127)
==== Problem 3 ====   
==== Problem 3 ====   
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* X ~ Binom(10, .9)
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For X � Bin(32; 0.81), simplify the equations by hand and then use SOCR to compute.
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* Find and verify:
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* P(X � 24 \(\cap \) X < 20)
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* P(5 < x < 8)
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* P(X � 24 \(\cup \) X < 20)
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* P(x < 8)
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* P(X > 23 \(\cup \) X < 30)
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* P(x ≤ 7)
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* P(x ≥ 9)
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==== Problem 4 ====
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* X ~ Binom(30, .1)
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* Find and verify: P(x > 2)
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===Distribution Comparison===
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* Graph and comment on the shape of the [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial distribution] with n = 30, p = 0.1 and then with n = 20, p = 0.9 (take a snapshot of both).
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* Now, keep n = 30 but change p = 0.45.  Now, let n = 100, p = 0.1.  Take a snapshot of both.
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* What changes do you observe in the distribution as the parameters change?  Write brief statements about the changes in a chart like this.
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{|border="1" cellpadding="20"
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|Smaller n
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|Larger n
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|Smaller p
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|Larger p
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|-
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|
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==== Problem 4 ==== 
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Plot the following distributions and take SNAPSHOTS of those denoted by (*):
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:Group A
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*� Bin(8; 0,2) (*)
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* � Bin(15; 0,2)
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�*� Bin(25; 0,2)
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�*� Bin(55; 0,2)
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�*� Bin(95; 0,2) (*)
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:Group B
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*� Bin(30; 0,05) (*)
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�*� Bin(30; 0,2)
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�* Bin(30; 0,5) (*)
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�*� Bin(30; 0,9) (*)
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�*� Bin(95; 1)
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|
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==== Problem 5 ==== 
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Use your snapshots from question 4 to answer the following questions:
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|
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* Describe how the distribution changes as the number of trials increases.
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|}
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* Describe how the distribution changes as the probability of success changes.
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* Write a few 'rules of thumbs' to help you remember the eff�ects of changing n and p.
<hr>
<hr>

Revision as of 14:33, 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
  • � Bin(8; 0,2) (*)
  • � Bin(15; 0,2)

�*� Bin(25; 0,2) �*� Bin(55; 0,2) �*� Bin(95; 0,2) (*)

Group B
  • � Bin(30; 0,05) (*)

�*� Bin(30; 0,2) �* Bin(30; 0,5) (*) �*� Bin(30; 0,9) (*) �*� 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 eff�ects of changing n and p.



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