Math 227 Practice Test 2 Sec 4.4-6.2 Name Find the indicated probability. ) A bin contains 64 light bulbs of which 0 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. A) 0 B) 0.484 C) 0.428 D) 0.844 2) In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary. A) 0.9 B) 2.64 C) 0.66 D) 0.06 3) Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places. A) 0.3333 B) 0.00000002 C) 0.0000075 D) 0.0082 4) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction. A) 2 3 B) 3 02 C) 663 D) 4 663 5) A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places. A) 0.009 B) 0.623 C) 0.6297 D) 0.0029 6) A sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. What is the probability that all four of the calculators selected are defective? Round to four decimal places. A) 0.463 B) 7.5098 C) 0.449 D) 0.390 7) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 425 38 35 498 Women 38 32 43 456 Total 806 70 78 954 If two different people are randomly selected from the 954 subjects, find the probability that they are both women. Round to four decimal places. A) 0.2282 B) 0.000004809 C) 0.595 D) 0.2285 Find the indicated probability. Round to the nearest thousandth. 8) A sample of 4 different calculators is randomly selected from a group containing 8 that are defective and 40 that have no defects. What is the probability that at least one of the calculators is defective? A) 0.774 B) 0.80 C) 0.785 D) 0.25
9) In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0., what is the probability that the mixture will test positive? A) 0.0000000 B) 0.469 C).00 D) 0.53 Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 0) The following table contains data from a study of two airlines which fly to Small Town, USA. Number of flights Number of flights which were on time which were late Podunk Airlines 33 6 Upstate Airlines 43 5 If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time. A) B) 76 76 87 C) 43 87 D) None of the above is correct. Find the mean of the given probability distribution. ) In a certain town, 30% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. x P(x) 0 0.240 0.46 2 0.2646 3 0.0756 4 0.008 A) µ =.20 B) µ = 2.00 C) µ =.44 D) µ =.0 Provide an appropriate response. Round to the nearest hundredth. 2) The probabilities that a batch of 4 computers will contain 0,, 2, 3, and 4 defective computers are 0.6274, 0.302, 0.0575, 0.0047, and 0.000, respectively. Find the standard deviation for the probability distribution. A) = 0.39 B) = 0.56 C) = 0.63 D) = 0.76 Answer the question. 3) Assume that there is a 0.5 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games? A) Yes B) No 2
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 4) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 39 6 65 57 Women 32 72 80 464 Total 703 33 45 98 If one of the 98 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that it is a woman. Round to the nearest thousandth. A) 0.38 B) 0.672 C) 0.444 D) 0.373 Solve the problem. 5) The library is to be given 3 books as a gift. The books will be selected from a list of 8 titles. If each book selected must have a different title, how many possible selections are there? A) 86 B) 4896 C) 5832 D) 54 6) How many ways can an IRS auditor select 3 of 9 tax returns for an audit? A) 729 B) 6 C) 504 D) 84 7) A state lottery involves the random selection of six different numbers between and 3. If you select one six number combination, what is the probability that it will be the winning combination? A) B) C) D) 530,22,320 887,503,68 720 736,28 8) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? A) 40,320 B) 20,60 C) 720 D) 48 9) A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are questions on the survey? A) 39,96,800 B) 3,628,800 C) D) 2 20) A class has 8 students who are to be assigned seating by lot. What is the probability that the students will be arranged in order from shortest to tallest? (Assume that no two students are the same height.) A) 0.00024802 B) 0.000984 C) 0.0000248 D) 0.000 Answer the question. 2) Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games? A) Yes B) No 3
22) Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are considered morbidly obese. Is it unusual to have no obese subjects among three randomly selected adolescents? x P(x) 0 0. 0.25 2 0.450 3 0.224 A) Yes B) No Provide an appropriate response. 23) Suppose you buy ticket for $ out of a lottery of,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) $0.00 B) -$0.50 C) -$0.40 D) -$.00 24) A 28-year-old man pays $8 for a one-year life insurance policy with coverage of $50,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? A) $49,90.00 B) -$80.89 C) $90.00 D) -$9.00 Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 25) Choosing 4 marbles from a box of 40 marbles (20 purple, 2 red, and 8 green) one at a time without replacement, keeping track of the number of red marbles chosen. A) Not binomial: there are more than two outcomes for each trial. B) Not binomial: there are too many trials. C) Procedure results in a binomial distribution. D) Not binomial: the trials are not independent. 26) Choosing 5 marbles from a box of 40 marbles (20 purple, 2 red, and 8 green) one at a time with replacement, keeping track of the colors of the marbles chosen. A) Not binomial: there are too many trials. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: the trials are not independent. D) Procedure results in a binomial distribution. 27) Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "6". A) Not binomial: the trials are not independent. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: there are too many trials. D) Procedure results in a binomial distribution.. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. 28) n = 7, x = 4, p = 0.5 A) 0.40 B) 0.063 C) 0.273 D) 0.355 Find the indicated probability. Round to three decimal places. 29) A machine has identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working. A) 0.949 B) 0. C) 0.62 D) 0.839 4
30) A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 7% rate of defects, what is the probability that this whole shipment will be accepted? A) 0.96 B) 0.535 C) 0.649 D) 0.279 Find the indicated probability. 3) A tennis player makes a successful first serve 5% of the time. If she serves 9 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others. A) 0.0635 B) 0.0084 C) 0.33 D) 0.54 Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 32) n = 676; p = 0.7 A) µ = 474.9 B) µ = 473.2 C) µ = 47.7 D) µ = 474.5 Find the indicated probability. 33) A slot machine at a hotel is configured so that there is a /200 probability of winning the jackpot on any individual trial. If a guest plays the slot machine 6 times, find the probability of exactly 2 jackpots. If a guest told the hotel manager that she had hit two jackpots in 6 plays of the slot machine, would the manager be surprised? A) 0.000000694; Yes, the probability of 2 jackpots in 6 plays is extremely small. B) 0.000004; Yes, the probability of 2 jackpots in 6 plays is extremely small. C) 0.000000692; Yes, the probability of 2 jackpots in 6 plays is extremely small. D) 0.0872; No, hitting 2 jackpots in 6 trials is not so unlikely. Find the standard deviation,, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 34) n = 38; p = 0.4 A) = 3.02 B) = 0.6 C) = 7.4 D) = 6.29 Use the given values of n and p to find the minimum usual value µ - 2 and the maximum usual value µ + 2. Round your answer to the nearest hundredth unless otherwise noted. 35) n = 237, p = 4 A) Minimum: 45.92; maximum: 72.58 B) Minimum: 52.58; maximum: 65.92 C) Minimum: 49.82; maximum: 68.68 D) Minimum: 72.58; maximum: 45.92 Solve the problem. 36) A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch. A) 0.2 B) 8 C).8 D) 5.8 Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2 or greater than µ + 2. 37) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 634 consumers who recognize the Dull Computer Company name? A) Yes B) No 5
38) According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 99 of the 2500 televisions are tuned to "Eyewitness News"? A) Yes B) No Use the Poisson Distribution to find the indicated probability. 39) The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.8. Find the probability that in a randomly selected year, the number of lightning strikes is 0. A) 0.029 B) 0.0224 C) 0.0380 D) 0.02 Find the indicated mean. 40) The mean number of homicides per year in one city is 2.4. Suppose a Poisson distribution will be used to find the probability that on a given day there will be fewer than 4 homicides. Find the mean of the appropriate Poisson distribution (the mean number of homicides per day). Round your answer to four decimal places. A) 5.35 B) 2.4 C) 0.0586 D) 0.42 Use the Poisson model to approximate the probability. Round your answer to four decimal places. 4) The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson distribution to approximate the probability that among,000 cars passing through this tunnel, at most two will have a flat tire. A) 0.9274 B) 0.0623 C) 0.9377 D) 0.0726 E) 0.9898 42) The rate of defects among CD players of a certain brand is.5%. Use the Poisson approximation to the binomial distribution to find the probability that among 430 such CD players received by a store, there are exactly three defective CD players. A) 0.060 B) 0.44 C) 0.0530 D) 0.9293 E) 0.0707 Using the following uniform density curve, answer the question. 43) What is the probability that the random variable has a value greater than 5? A) 0.250 B) 0.375 C) 0.325 D) 0.500 44) What is the probability that the random variable has a value less than 2.7? A) 0.0875 B) 0.4625 C) 0.225 D) 0.3375 45) What is the probability that the random variable has a value between 5.3 and 5.7? A) 0.750 B) 0.3000 C) 0.0750 D) 0.0500 Assume that the weight loss for the first month of a diet program varies between 6 pounds and 2 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. 46) Between 8 pounds and pounds A) 3 B) 2 C) 2 3 D) 4 6
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation. 47) Shaded area is 0.090. A) -.39 B) -.45 C) -.26 D) -.34 48) Shaded area is 0.0694. A).39 B).45 C).48 D).26 49) Shaded area is 0.8599. A) 0.5557 B) 0.805 C).08 D) -.08 If z is a standard normal variable, find the probability. 50) The probability that z lies between 0 and 3.0 A) 0.503 B) 0.9987 C) 0.4987 D) 0.27 5) The probability that z is less than.3 A) 0.8907 B) 0.292 C) 0.8485 D) 0.8708 52) The probability that z is greater than -.82 A) 0.0344 B) 0.9656 C) 0.4656 D) -0.0344 The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 C (denoted by negative numbers) and some give readings above 0 C (denoted by positive numbers). Assume that the mean reading is 0 C and the standard deviation of the readings is.00 C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 53) Find P96, the 96th percentile. A).03 B).75 C) -.38 D).82 7
54) If 7% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. A).45 B).26 C).48 D).39 55) A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the reading that separates the bottom 4% from the others. A) -.75 B) -.48 C) -.63 D) -.89 Find the indicated value. 56) z0.005 A) 2.575 B) 2.05 C) 2.835 D) 2.535 8
Answer Key Testname: MATH 227 PRACTICE TEST 2 WINTER 207 ) C 2) A 3) C 4) D 5) B 6) D 7) A 8) C 9) B 0) B ) A 2) C 3) B 4) B 5) A 6) D 7) D 8) B 9) A 20) C 2) A 22) B 23) B 24) D 25) D 26) B 27) D 28) C 29) D 30) C 3) D 32) B 33) B 34) A 35) A 36) A 37) A 38) B 39) B 40) C 4) E 42) E 43) B 44) D 45) D 46) B 47) D 48) C 49) D 50) C 9
Answer Key Testname: MATH 227 PRACTICE TEST 2 WINTER 207 5) D 52) B 53) B 54) C 55) A 56) A 0