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Understanding Binomial Distribution in Probability

Learn about the binomial distribution, key concepts, and examples for successful outcomes in probability problems with only two possible results. Explore Bluman's chapter on Binomial Distribution. Practice and apply your knowledge with assigned problems.

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Understanding Binomial Distribution in Probability

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  1. This week • Quiz tomorrow on 5-1 and 5-2 • Today 5-3 • Tuesday Finish 5-3 and practice • Wednesday Review • Thursday 1st part of test • Monday 2nd part of test and start Ch 14

  2. HW?s

  3. 5-3 The Binomial Distribution • Many types of probability problems have only two possible outcomes or they can be reduced to two outcomes. • Examples include: when a coin is tossed it can land on heads or tails, when a baby is born it is either a boy or girl, etc. Bluman, Chapter 5 3

  4. The Binomial Distribution • The binomial experiment is a probability experiment that satisfies these requirements: • Each trial can have only two possible outcomes—success or failure. • There must be a fixed number of trials. • The outcomes of each trial must be independent of each other. • The probability of success must remain the same for each trial. Bluman, Chapter 5 4

  5. Notation for the Binomial Distribution P(S) P(F) p q P(S) = p n X Note that X = 0, 1, 2, 3,...,n The symbol for the probability of success The symbol for the probability of failure The numerical probability of success The numerical probability of failure and P(F) = 1 – p = q The number of trials The number of successes Bluman, Chapter 5 5

  6. The Binomial Distribution In a binomial experiment, the probability of exactly X successes in n trials is Bluman, Chapter 5 6

  7. Why? Bluman, Chapter 5 7

  8. Example 5-16: Survey on Doctor Visits A survey found that one out of five Americans say he or she has visited a doctor in any given month. If 10 people are selected at random, find the probability that exactly 3 will have visited a doctor last month. Bluman, Chapter 5 8

  9. Chapter 5Discrete Probability Distributions Instead of “exactly”, “at least”… Bluman, Chapter 5 9

  10. Example 5-17: Survey on Employment A survey from Teenage Research Unlimited (Northbrook, Illinois) found that 30% of teenage consumers receive their spending money from part-time jobs. If 5 teenagers are selected at random, find the probability that at least 3 of them will have part-time jobs. Bluman, Chapter 5 10

  11. Chapter 5Discrete Probability Distributions The Lazy Man’s Way (No, you will not be able to do this on a test.) Bluman, Chapter 5 11

  12. Example 5-18: Tossing Coins A coin is tossed 3 times. Find the probability of getting exactly two heads, using Table B. Bluman, Chapter 5 12

  13. Practice • Do a, b, c on your note sheet • Read the last part of your note sheet “IN YOUR CALC” and enter the info into your calculator to check your results.

  14. The Binomial Distribution The mean, variance, and standard deviation of a variable that has the binomial distribution canbe found by using the following formulas. Bluman, Chapter 5 14

  15. Chapter 5Discrete Probability Distributions Finding mean, variance and standard deviation Bluman, Chapter 5 15

  16. Example 5-23: Likelihood of Twins The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would result in twins. Bluman, Chapter 5 16

  17. Practice • Complete the two examples on your note sheet for mean, variance, and standard deviation.

  18. Assignment • CW: Pg 277-278: 11, 24 • HW: 277-278: 1, 2, 4, 6, 7, 10, 13, 15, 18, 20, 23, 26, 29, 30

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