SOCR Courses 2012 2013 Stat13 1 Lab3

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 effects of changing n and p.

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

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