Section 5-3

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Section 5-3. Binomial Probability Distributions. What does the prefix “Bi” mean?. We will now consider situations where there are exactly two outcomes: Yes/no to a survey question Product is defective/not defective Correct/Wrong response to a multiple choice question

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## Section 5-3

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### Section 5-3

Binomial Probability Distributions

What does the prefix “Bi” mean?

We will now consider situations where there are exactly two outcomes:

• Yes/no to a survey question
• Product is defective/not defective
• Correct/Wrong response to a multiple choice question
• Arrival time for an airline is on time/not on time
Conditions for a Binomial Probability Distribution
• There are a fixed number of trials, n, that are identical and independent.
• Each trial has exactly 2 outcomes: success, S or failure, F
• The probability of success must remain the same for each trial.
Notation:

P(S) = p

P(F) = 1 – p = q

n = # of trials

x = # of successes

*success is just what is being measured

Example 1

Determine whether the given procedure results in a binomial distribution.

• Determining whether each of 3000 heart pacemakers is acceptable or defective.
• Surveying people and asking them what they think of the current president.
• Spinning the roulette wheel 12 times and finding the number of times that the outcome is an odd number.
Methods for finding binomial probabilities
• Binomial Probability Formula:
• Table A-1, Appendix A
• MINITAB
Example 2

A report from the Secretary of Health and Human Services stated that 70% of single-vehicle traffic fatalities that occur at night on weekends involve an intoxicated driver. If a sample of 10 single-vehicle traffic fatalities that occur at night on a weekend is selected, find the probability that exactly seven involve a driver that is intoxicated.

This is a binomial experiment where:

n = 10 x = 7 p = 0.70 q = 0.30

How about the probability of at least 8 involving an intoxicated driver?

P(at least 8) = P(8) or P(9) or P(10)

= 0.233474 + 0.121061 + 0.028248

=0.382783

Example 3

In a clinical test of the drug Viagra, it was found that 4% of those in a placebo group experienced headaches.

• Assuming that the same 4% rate applies to those taking Viagra, find the probability that among eight Viagra users, three experience headaches.