# 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== | ||

- | You can access the applet for any of the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html SOCR distributions] | + | 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 ==== | ||

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

- | * | + | * P(X = 7) |

+ | * E(X) | ||

+ | * SD(X) | ||

- | ==== Problem 2 ==== | + | ==== Problem 2 ==== |

- | + | 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(39 < X < 127) | ||

==== Problem 3 ==== | ==== 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( | + | * P(X � 24 \(\cup \) X < 20) |

- | + | * P(X > 23 \(\cup \) X < 30) | |

- | * P( | + | |

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+ | ==== 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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## 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.

- SOCR Home page: http://www.socr.ucla.edu

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