# SOCR Courses 2012 2013 Stat13 1 Lab3

(Difference between revisions)
 Revision as of 14:37, 22 April 2013 (view source)IvoDinov (Talk | contribs) (→Problem 4)← Older edit Revision as of 14:38, 22 April 2013 (view source)IvoDinov (Talk | contribs) (→Problem 4)Newer edit → Line 28: Line 28: Plot the following distributions and take SNAPSHOTS of those denoted by (*): Plot the following distributions and take SNAPSHOTS of those denoted by (*): :Group A :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 :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) *X~ Bin(95; 1)

## 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
• X ~ Bin(8; 0.2) (*)
• X ~ Bin(15; 0.2)
• X~ Bin(25; 0.2)
• X~ Bin(55; 0.2)
• X~ Bin(95; 0.2) (*)
Group B
• X~ Bin(30; 0.05) (*)
• X~ Bin(30; 0.2)
• X~ Bin(30; 0.5) (*)
• X~ Bin(30; 0.9) (*)
• X~ 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.