SOCR Courses 2012 2013 Stat13 1 Lab3
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 >= 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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