# SOCR Courses 2012 2013 Stat13 1 Lab3

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## 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 >= 146)
- P(153 < X < 178)

#### 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 effects of changing n and p.

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

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