Binomial Probability Distributions. Binomial Probability Distributions are important because they allow us to deal with circumstances in which the outcomes.

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Presentation transcript:

Binomial Probability Distributions

Binomial Probability Distributions are important because they allow us to deal with circumstances in which the outcomes belong to two relevant categories, such as: True or False Heads or Tails Boy or Girl Right or Wrong

A binomial probability distribution results from a procedure that meets all the following requirements: 1. The procedure has a fixed number of trials. 2.The trials must be independent. (The outcome of any individual trial doesn’t affect the probabilities in the other trials.) 3.Each trial must have all outcomes classified into two categories. 4.The probabilities must remain constant for each trial.

State whether the given procedure results in a binomial distribution. 1.Guessing the correct answer to 50 multiple choice questions, then determining whether answers are right or wrong. 2.Rolling a die 50 times. 3.Rolling a die 50 times and finding the number of times 5 occurs. 4.Counting the number of girls out of the next 20 born at Roper Hospital. 5.Joe buys a state lottery ticket every week. The count X is the number of times in a year he wins a prize.

NOTATION

Formula: The probability of exactly X successes in n trials is:

A coin is tossed 4 times. Find the probability of getting exactly two tails. Is this binomial? If so, find the probability.

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.

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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 15 single-vehicle traffic fatalities that occur at night on a weekend is selected, find the probability that exactly 12 involve a driver who is intoxicated.

Public Opinion reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is selected, find these probabilities using your calculator: a.There are exactly 5 people in the sample who are afraid of being alone at night. b.There are at most 3 people in the sample who are afraid of being alone at night. c.There are at least 15 people in the sample who are afraid of being alone at night. d.There are at least 4 people in the sample who are afraid of being alone at night.