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AP Statistics: Section 8.1A Binomial Probability

AP Statistics: Section 8.1A Binomial Probability.

james-sexton
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AP Statistics: Section 8.1A Binomial Probability

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  1. AP Statistics: Section 8.1ABinomial Probability

  2. There are four conditions to a binomial setting:1. Each observation falls into one of just two categories: _________ or ________.2. There is a ______ number of observations, __.3. These n observations are all ____________.4. The probability of success, __, is _________ for each observation.

  3. If data are produced in a binomial setting, then the random variable X = the number of successes is called a binomial random variable and the probability distribution of X is called a binomial distribution which is abbreviated ______.

  4. Example 1: Determine if each of the following situations is a binomial setting. If so, state the probability distribution for X. If not, state which of the 4 conditions above is not met.

  5. Situation 1: Blood type is inherited. If both parents carry genes for the O and A blood types, each child has probability 0.25 of getting two O genes and so having blood type O. A couple’s 5 different children inherit independently of each other. Let X = number of children with type O blood.

  6. Situation 2: Deal 10 cards from a shuffled deck and let X = the number of red cards.

  7. Situation 3: An engineer chooses a SRS of 10 switches from a shipment of 10,000 switches. Suppose that (unknown to the engineer) 10% of the switches in the shipment are bad. Let X = the number of bad switches in the sample. ****When choosing an SRS from a population that is much larger than the sample, the observations are considered independent.

  8. Binomial Probability: If X has a binomial distribution with n observations and probability p of success on each observation, the possible values of X are 0, 1, 2, 3, . . . , n. If k is any one of these values, then

  9. The notation is read n choose k and means the number of possible ways to choose k objects from a group of n objects.It is also written _____

  10. Example 2 (combinations): How many different ways can we choose a subcommittee of size 3 from a student council that has 7 members?

  11. Example 3: You randomly guess the answers to10 multiple choice questions which have 5 possible answers. What is the probability of getting exactly 6 correct answers?

  12. Binomial Probability on the TI83/84:

  13. Example 4: Consider situation 3 in example 1. Find the probability that in an SRS of size 10, no more than 1 switch fails.

  14. Example 5: Corinne is a basketball player who makes 75% of her free throws over the course of a season. In a big game, Corinne shoots 12 free throws and makes only 5 of them. Is it unusual for Corinne to perform this poorly?Note: We actually want the probability of making a basket onat most 5 free throws. Cumulative Binomial Probability on the TI83/84:

  15. Any difference in answers between the manual calculation and using your calculator is due to rounding error.

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