1 / 12

Section 5-3

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

benjamin
Download Presentation

Section 5-3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 5-3 Binomial Probability Distributions

  2. 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

  3. 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.

  4. Notation: P(S) = p P(F) = 1 – p = q n = # of trials x = # of successes *success is just what is being measured

  5. 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.

  6. Methods for finding binomial probabilities • Binomial Probability Formula: • Table A-1, Appendix A • MINITAB

  7. 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

  8. Using table generated in MINITAB P(7) = 0.266828

  9. 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

  10. 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.

More Related