Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
SWBAT: Compute and interpret probabilities involving binomial random variables. Lesson 6-6 Do Now: A sunglasses company sells two distinct brands of glasses. Type A sells 82% of the time for $37. Type B sells 18% of the time for $87. What is the expected value for each of the sunglasses sold? (A) $15.66 (B) $30.34 (C ) $46.00 (D) $62.00 (E) $124.00 How do we determine a BINOMIAL setting?? A binomial setting arises when we perform several independent trials of the same chance process and record the number of times that a particular outcome occurs. The four conditions for a binomial setting are: B I inary? The possible outcomes of each trial can be classified as “success” or “failure.” ndependent? Trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial. N S umber? The number of trials n of the chance process must be fixed in advance. uccess? On each trial, the probability p of success must be the same. SWBAT: Compute and interpret probabilities involving binomial random variables. Lesson 6-6 BINOMIAL PROBABILITY Binomial Probability Calculator Steps binompdf(n,p,k) computes P(X = k) binomcdf(n,p,k) computes P(X ≤ k) Example: Each child of a particular pair of parents has probability 0.25 of having type O blood. Suppose the parents have 5 children. (a) Find the probability that exactly 3 of the children have type O blood. (b) Should the parents be surprised if more than 3 of their children have type O blood? Justify your answer. SWBAT: Compute and interpret probabilities involving binomial random variables. Lesson 6-6 You Try!! To introduce her class to binomial distributions, Mrs. Desai gives a 10-item, multiple-choice quiz. The catch is, students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer’s random number generator to produce the answer key, so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let X = the number of Patti’s correct guesses. (a) Show that X is a binomial random variable. (b) Find P(X = 3). Explain what this result means. (c) To get a passing score on the quiz, a student must guess correctly at least 6 times. Would you be surprised if Patti earned a passing score? C ompute an appropriate probability to support your answer. SWBAT: Compute and interpret probabilities involving binomial random variables. Lesson 6-6 LESSON PRACTICE For Questions 1 & 2, explain whether the given random variable has a binomial distribution. 1. Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants them in her garden. Let X = the number of seeds that germinate. 2. Exactly 10% of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let V = the number of students chosen. 3. In the United States, 44% of adults have type O blood. Suppose we choose 7 U.S. adults at random. Let X = the number who have type O blood. (a) Use the binomial probability formula to find P(X = 4). Interpret this result in context. (b) How surprising would it be to get more than 4 adults with type O blood in the sample? C alculate an appropriate probability to support your answer. SWBAT: Compute and interpret probabilities involving binomial random variables. Lesson 6-6 LESSON PRACTICE 4. Suppose you purchase a bundle of 10 bare-root rhubarb plants. The sales clerk tells you that on average you can expect 5% of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let Y = the number of plants that die before producing any rhubarb. (a) Use the binomial probability formula to find P(Y = 1). Interpret this result in context. (b) Would you be surprised if 3 or more of the plants in the bundle die before producing any rhubarb? C alculate an appropriate probability to support your answer. 5. Seed Depot advertises that 85% of its flower seeds will germinate(grow). Suppose that the company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants them in her garden. Let X = the number of seeds that germinate. (a) Find the probability that exactly 17 seeds germinate. Show your work. (b) If only 12 seeds actually germinate, should Judy be suspicious that the company’s claim is not true? C ompute P(X ≤ 12) and use this result to support your answer.