SWBAT: Find the mean and standard deviation of a binomial random variable Lesson 6-8 Do Now: A pharmaceutical lab claims that a drug it produces causes serious side effects in 20 out of every 1000 people on average. To check his claim, a hospital administers the drive to 15 randomly selected patients and finds that 3 suffer from side effects. If the lab’s claims are correct, what is the probability of the hospital obtaining the results it did? Mean and Standard Deviation of a Binomial Random Variable If a count X has the binomial distribution with number of trials n and probability of success p, the mean and standard deviation of X are = = √ ( − ) SWBAT: Find the mean and standard deviation of a binomial random variable Lesson 6-8 Example: Mr. Bullard’s AP Statistics class did an activity to determine whether or not you can taste a difference between tap water and bottled water. There are 21 students in the class. If we assume that the students in his class cannot tell tap water from bottled water, then each one is basically guessing, with a 1/3 chance of being correct. Let X = the number of students who correctly identify the cup containing the different type of water. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) Of the 21 students in the class, 13 made correct identifications. Are you convinced that Mr. Bullard’s students can tell bottled water from tap water? Justify your answer. SWBAT: Find the mean and standard deviation of a binomial random variable Lesson 6-8 You Try/Lesson Practice!! 1. Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. C ompany engineers test an SRS of 350 engines of this model. Let X = the number that operate for an hour without failure. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) Two engines failed the test. Are you convinced that this model of engine is less reliable than it’s supposed to be? C ompute P(X ≤ 348) and use the result to justify your answer. SWBAT: Find the mean and standard deviation of a binomial random variable Lesson 6-8 2. 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) Find . Interpret this value in context. (b) Find . Interpret this value in context. (c) What’s the probability that the number of Patti’s correct guesses is more than 2 standard deviations above the mean? Show your method. SWBAT: Find the mean and standard deviation of a binomial random variable Lesson 6-8 3. When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls. Let X = the number of calls that reach a live person. (a) Find and interpret . (b) Find and interpret . 4. A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X= the number of people who the lie detector says are being deceptive. (a) Find and interpret . (b) Find and interpret .
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