Binomial Probability Practice Study Guide With Questions And Answers.

According to a CBS/New York Times poll taken in 1992, 15% of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability that exactly two have responded to a call-in poll? - correct answer binompdf(5, .15, 2) = 0.1382 According to a medical study, 40% of people will experience an adverse side effect within one hour after taking a particular experimental drug. Suppose you survey 15 people who participated in the study. What is the probability that at least 8 of them experienced an adverse effect? - correct answer P(X≥8)= 1 - binomcdf(15, 0.4, 7) = 0.2131 In a certain mechanical system, 5 bulbs are used and will operate if at least three are functioning properly. Given that 15% of bulbs are defective, what is the probability that the system will malfunction? - correct answer P(X3) = binomcdf(5, .15, 2)= .9734 An automobile-safety researcher, Kathryn, claims that 1 in 10 automobile accidents are caused by driver fatigue. What is the probability that at most three out of five automobile accidents are caused by driver fatigue? - correct answer P(X≤3)=binomcdf(5, .10, 3)=.9995 If you had no idea how to do any of the problems on a 10 question multiple choice quiz and you chose to randomly select your answer, what is the probability you would get 70% of them correct? (assume there are 4 choices per question). - correct answer P(X=7) = binompdf(10, .24, 7) = 0.003 If you had no idea how to do any of the problems on a 10 question multiple choice quiz and you chose to randomly select your answer, what would the probability be that you got a 70% or better on the exam? - correct answer P(X ≥7)= 1 - binomcdf(10, .25, 6) = .004 A pet food manufacturer is promoting a new brand with a rebate offer on its 10-pound bag. Each package is supposed to contain a coupon for a $4.00 mail-in rebate. The company has found that the machine dispensing these coupons fails to place a coupon in 10 percent of the bags. If a dog owner buys 5 bags, find the probability that at least 1 bag will fail to have a coupon. - correct answer P(X≥1)= 1 - binompdf(5, .10, 0) = 0.4095 A survey found that "Business" was the most popular college major for college students who played basketball or football, with 37 percent selecting this major. Find the probability that a random sample of 500 male college athletes in these 2 sports would contain more than 200 business majors. - correct answer P(X200)= 1 - binomcdf(500, .37, 200) = 0.076 Safety-tipped wooden matches are more difficult to light than regular matches. A manufacturer has found that 25 percent of its safety-tipped matches fail to ignite on the first strike. Find the probability that in a box of 20 matches, 10 to 15 will fail to ignite on the first strike. - correct answer P(10≤X≤15) = binomcdf(20, .25, 15) - binomcdf(20, .25, 9) = 0.0139 A restaurant has found that about 1 customer in 5 will order a dessert with a meal. If the restaurant serves 580 meals on a certain day, find the probability that over 125 will be accompanied by dessert. - correct answer P(X125) = 1 - binomcdf(580, .20, 125) = .1619 A NASA official estimated that there is a probability of 1/78 that any single space shuttle flight will result in a catastrophic failure. Find the probability that for the next 10 flights there will be no shuttle disaster? - correct answer P(X=0) = binompdf(10, 1/78, 0) = 0.8789 A 1996 study found that about 1 in 5 Americans suffered from some form of mental illness during the course of a year. If 20 adults are selected at random, find the probability that a. exactly 4 will experience some type of mental illness. - correct answer P(x=4) = binompdf(20, .20, 4) = 0.2182 Statistics from the Federal Highway Administration show that 45% of the time there will be occupant injuries when vehicle accidents are caused by running a red light. In an investigation of 75 accidents triggered by running a red light, what is the probability a. that occupant injuries occurred in more than 36 cases? - correct answer P(x36)= 1 - binomcdf(75, .45, 36) = 0.261