# SOCR Courses 2012 2013 Stat13 1 Lab3

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 Revision as of 01:46, 26 February 2013 (view source)IvoDinov (Talk | contribs) (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…')← Older edit Revision as of 14:33, 22 April 2013 (view source)IvoDinov (Talk | contribs) Newer edit → 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.

## 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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