Properties of the Binomial Probability Distributions 1- The experiment consists of a sequence of n identical trials 2- Two outcomes (SUCCESS and FAILURE.

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Properties of the Binomial Probability Distributions 1- The experiment consists of a sequence of n identical trials 2- Two outcomes (SUCCESS and FAILURE ) are possible on each trial 3- The probability of success, denoted by p, does not change from trial to trial. Consequently, the probability of failure, denoted by q and equals to 1-p, does not change from trial to trial 4- The trials are independent.

Example :4 Fitness Test The Heart Association claims that only 10% of adults over 30 can pass the minimum requirements of Fitness Test. Suppose four adults are randomly selected and each is given the fitness test. Use the formula for a binomial random variable to find the probability distribution of x, where x is the number of adults who pass the fitness test. Graph the distribution.

According to a research only 5% of the cigarette smokers enter into a treatment program to help them quit smoking. In a random sample of 200 smokers, let x be the number who enter into a treatment program. A-) Explain why x is a binomial r.v. B-) What is the value of p? Interpret this value. c-) What is the expected value of x? Interpret this value.

Example: Purchase Decision Consider the purchase decisions of the next three customers who enter the clothing store. On the basis of past experience, the store manager estimates the probability that any one customer will make a purchase is 0.30 Q: What is the probability that two of the next three customers will make a purchase?

Example: 1 Test the following function to determine whether it is a probability function. If it is not, try to make it into a probability function S(x) = (6 - |x – 7|) / 36, for x = 2, 3, 4, 5, 6, 7,..., 11, 12 a. List the distribution of probabilities and sketch a histogram. b. Do you recognize S(x)? If so, identify it.

Example: 2 The College Board website provides much information for students, parents, and professionals with respect to the many aspects involved in Advanced Placement (AP) courses and exams. One particular annual report provides the percent of students who obtain each of the possible AP grades (1 through 5). The 2008 grade distribution for all subjects was as follows: AP Grade Percent a. ) Express this distribution as a discrete probability distribution. b. ) Find the mean and standard deviation of the AP exam scores for 2008.

Example :4 Fitness Test The Heart Association claims that only 10% of adults over 30 can pass the minimum requirements of Fitness Test. Suppose four adults are randomly selected and each is given the fitness test. Use the formula for a binomial random variable to find the probability distribution of x, where x is the number of adults who pass the fitness test. Graph the distribution.