SOCR Courses 2012 2013 Stat13 1 Lab3

From Socr

(Difference between revisions)
Jump to: navigation, search
(Created page with '== Stats 13.1 - Laboratory Activity 3== You can access the applet for any of the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SO…')
Line 1: Line 1:
== [[SOCR_Courses_2012_2013_Stat13_1 | Stats 13.1]] - Laboratory Activity 3==
== [[SOCR_Courses_2012_2013_Stat13_1 | Stats 13.1]] - Laboratory Activity 3==
-
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.
+
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.
 +
 
 +
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 ====   
-
* X ~ Binom(10, .5)
+
Suppose X ~ Binomial(10, 0.5) compute by hand:
-
* Find: P(X = 3), E(X), sd(X) from the SOCR output, and verify them with the formulas discussed in class.
+
* P(X = 7)
 +
* E(X)
 +
* SD(X)
-
==== Problem 2 ====  
+
==== Problem 2 ====
-
* X ~ Binom(10, .1)
+
For X � Binomial(250; 0.65), use [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html SOCR Distributions] to compute:
-
* Find P(1 ≤ X ≤ 3) from SOCR, and verify using the binomial formula.
+
* P(X = 146)
 +
* P(X >=237)
 +
* P(39 < X < 127)
==== Problem 3 ====   
==== Problem 3 ====   
-
* X ~ Binom(10, .9)
+
For X � Bin(32; 0.81), simplify the equations by hand and then use SOCR to compute.
-
* Find and verify:
+
* P(X � 24 \(\cap \) X < 20)
-
* P(5 < x < 8)
+
* P(X � 24 \(\cup \) X < 20)
-
* P(x < 8)
+
* P(X > 23 \(\cup \) X < 30)
-
* P(x ≤ 7)
+
-
* P(x ≥ 9)
+
-
 
+
-
==== Problem 4 ====
+
-
* X ~ Binom(30, .1)
+
-
* Find and verify: P(x > 2)
+
-
 
+
-
===Distribution Comparison===
+
-
 
+
-
* 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).
+
-
* Now, keep n = 30 but change p = 0.45.  Now, let n = 100, p = 0.1.  Take a snapshot of both.
+
-
* What changes do you observe in the distribution as the parameters change?  Write brief statements about the changes in a chart like this.
+
-
 
+
-
 
+
-
{|border="1" cellpadding="20"
+
-
|Smaller n
+
-
|Larger n
+
-
|Smaller p
+
-
|Larger p
+
-
|-
+
-
|
+
-
 
+
-
 
+
-
 
+
-
 
+
-
 
+
-
 
+
-
 
+
-
 
+
-
 
+
 +
==== 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.
<hr>
<hr>

Revision as of 14:35, 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.



Translate this page:

(default)

Deutsch

Español

Français

Italiano

Português

日本語

България

الامارات العربية المتحدة

Suomi

इस भाषा में

Norge

한국어

中文

繁体中文

Русский

Nederlands

Ελληνικά

Hrvatska

Česká republika

Danmark

Polska

România

Sverige

Personal tools