SOCR Courses 2012 2013 Stat13 1 Lab3 - Revision history

IvoDinov: /* Problem 2 */

2013-04-22T17:00:45Z

‎Problem 2

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‎Problem 2

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‎Problem 5

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‎Problem 4

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‎Problem 4

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‎Problem 3

IvoDinov at 14:41, 22 April 2013

2013-04-22T14:41:47Z

IvoDinov: 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…'

2013-02-26T01:54:39Z

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…'

New page

== [[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.

===[http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial Distribution] Activity ===

==== Problem 1 ====
* X ~ Binom(10, .5)
* Find: P(X = 3), E(X), sd(X) from the SOCR output, and verify them with the formulas discussed in class.

==== Problem 2 ====
* X ~ Binom(10, .1)
* Find P(1 ≤ X ≤ 3) from SOCR, and verify using the binomial formula.

==== Problem 3 ====
* X ~ Binom(10, .9)
* Find and verify:
* P(5 < x < 8)
* P(x < 8)
* 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
|-
|

|
|
|
|}

<hr>
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_Courses_2012_2013_Stat13_1_Lab3}}

@@ Line 16: / Line 16: @@
 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 >=237)
+* P(X >= 146)
-* P(39 < X < 127)
+* P(153 < X < 178)
 ==== Problem 3 ====

@@ Line 14: / Line 14: @@
 ==== Problem 2 ====
-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 >=237)

@@ Line 44: / Line 44: @@
 * 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.
+* Write a few 'rules of thumbs' to help you remember the effects of changing n and p.
 <hr>

@@ Line 28: / Line 28: @@
 Plot the following distributions and take SNAPSHOTS of those denoted by (*):
 :Group A
-* X ~ Bin(8; 0,2) (*)
+* X ~ Bin(8; 0.2) (*)
-* X ~ Bin(15; 0,2)
+* X ~ Bin(15; 0.2)
-*X~ Bin(25; 0,2)
+*X~ Bin(25; 0.2)
-*X~ Bin(55; 0,2)
+*X~ Bin(55; 0.2)
-*X~ Bin(95; 0,2) (*)
+*X~ Bin(95; 0.2) (*)
 :Group B
-*X~ Bin(30; 0,05) (*)
+*X~ Bin(30; 0.05) (*)
-*X~ Bin(30; 0,2)
+*X~ Bin(30; 0.2)
-*X~ Bin(30; 0,5) (*)
+*X~ Bin(30; 0.5) (*)
-*X~ Bin(30; 0,9) (*)
+*X~ Bin(30; 0.9) (*)
 *X~ Bin(95; 1)

@@ Line 28: / Line 28: @@
 Plot the following distributions and take SNAPSHOTS of those denoted by (*):
 :Group A
-*� Bin(8; 0,2) (*)
+* X ~ Bin(8; 0,2) (*)
-* � Bin(15; 0,2)
+* X ~ Bin(15; 0,2)
-�*� Bin(25; 0,2)
+*X~ Bin(25; 0,2)
-�*� Bin(55; 0,2)
+*X~ Bin(55; 0,2)
-�*� Bin(95; 0,2) (*)
+*X~ Bin(95; 0,2) (*)
 :Group B
-*� Bin(30; 0,05) (*)
+*X~ Bin(30; 0,05) (*)
-�*� Bin(30; 0,2)
+*X~ Bin(30; 0,2)
-�* Bin(30; 0,5) (*)
+*X~ Bin(30; 0,5) (*)
-�*� Bin(30; 0,9) (*)
+*X~ Bin(30; 0,9) (*)
-�*� Bin(95; 1)
+*X~ Bin(95; 1)
 ==== Problem 5 ====

@@ Line 20: / Line 20: @@
 ==== Problem 3 ====
-For X � Bin(32; 0.81), simplify the equations by hand and then use SOCR to compute.
+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 \(\cap \) X < 20)
-* P(X � 24 \(\cup \) X < 20)
+* P(X >= 24 \(\cup \) X < 20)
 * P(X > 23 \(\cup \) X < 30)

@@ Line 1: / Line 1: @@
 == [[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.
 ===[http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial Distribution] Activity ===
 ==== 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)
 ==== 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)
 ==== 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)
+==== 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.
 <hr>