Section 5.2 Binomial Distribution HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All

Section 5.2

Binomial Distribution

HAWKES LEARNING SYSTEMS

math courseware specialists

Copyright © 2008 by Hawkes Learning

Systems/Quant Systems, Inc.

All rights reserved.

• Binomial distribution – a special discrete probability function for problems with a fixed number of trials, where each trial has only two possible outcomes, and one of these outcomes is counted.

• Success – the outcome that is counted.



Definitions:

Probability Distribution

5.2 Binomial Distribution

x the number of successesn the number of trialsp the probability of getting a success on any trial

When calculating the binomial distribution, round your answers to three decimal places.

1. The experiment consists of a fixed number of identical trials, n.

2. Each trial is independent of the others.

3. For each trial, there are only two possible outcomes. For counting purposes, one outcome is labeled a success, the other a failure.

4. For every trial, the probability of getting a success is called p. The probability of getting a failure is then 1 – p.

5. The binomial random variable, X, is the number of successes in n trials.



Binomial Distribution Guidelines:



What is the probability of getting exactly 7 tails in 18 coin tosses?

Determine the probability:



Solution:

n 18, p 0.5, x 7





TI-84 Plus Instructions:

1. Press 2nd, then VARS

2. Choose 0: binompdf(

3. The format for entering the statistics is binompdf(n,p,x)



In the previous example we could have entered binompdf(18,0.5,7).

A quality control expert at a large factory estimates that 10% of all batteries produced are defective. If a sample of 20 batteries are taken, what is the probability that no more than 3 are defective?




Solution:

n 20, p 0.1, x 3, but this time we need to look at the probability that no more than three are defective, which is P(X ≤ 3).

P(X ≤ 3) P(X 0) P(X 1) P(X 2) P(X 3)



20C0(0.1)0(0.9)20 20C1(0.1)1(0.9)19

20C2(0.1)2(0.9)1820C3(0.1)3(0.9)17

0.867



TI-84 Plus Instructions:

1. Press 2nd, then VARS

2. Choose A: binomcdf(

3. The format for entering the statistics is binomcdf(n,p,x)



In the previous example we could have entered binomcdf(20,0.1,3).

A quality control expert at a large factory estimates that 20% of all batteries produced are defective. If a sample of 10 batteries are taken, what is the probability that more than 1 are defective?




Solution:

n 10, p 0.2, x 1, but this time we need to look at the probability that more than one are defective, which is P(X > 1).



P(X > 1) 1 P(X ≤ 1)

1 10C0(0.2)0(0.8)10 10C1(0.2)1(0.8) 9

0.624

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Section 5.2 Binomial Distribution HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All