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

2. 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. HAWKES LEARNING SYSTEMS math courseware specialists Definitions: Probability Distribution 5.2 Binomial Distribution x  the number of successes n  the number of trials p  the probability of getting a success on any trial When calculating the binomial distribution, round your answers to three decimal places.

3. 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. HAWKES LEARNING SYSTEMS math courseware specialists Binomial Distribution Guidelines: Probability Distribution 5.2 Binomial Distribution

4. What is the probability of getting exactly 7 tails in 18 coin tosses? Determine the probability: HAWKES LEARNING SYSTEMS math courseware specialists Solution: n  18, p  0.5, x  7 Probability Distribution 5.2 Binomial Distribution

5. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose 0: binompdf( 3.The format for entering the statistics is binompdf(n,p,x) Probability Distribution 5.2 Binomial Distribution In the previous example we could have entered binompdf(18,0.5,7).

6. 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? Determine the probability: HAWKES LEARNING SYSTEMS math courseware specialists 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) Probability Distribution 5.2 Binomial Distribution  20 C 0 (0.1) 0 (0.9) 20  20 C 1 (0.1) 1 (0.9) 19  20 C 2 (0.1) 2 (0.9) 18  20 C 3 (0.1) 3 (0.9) 17  0.867

7. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose A: binomcdf( 3.The format for entering the statistics is binomcdf(n,p,x) Probability Distribution 5.2 Binomial Distribution In the previous example we could have entered binomcdf(20,0.1,3).

8. 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? Determine the probability: HAWKES LEARNING SYSTEMS math courseware specialists 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). Probability Distribution 5.2 Binomial Distribution P(X > 1)  1  P(X ≤ 1)  1  10 C 0 (0.2) 0 (0.8) 10  10 C 1 (0.2) 1 (0.8) 9  0.624