Record on a ScanTron, your choosen response for each question. You may write on this form. One page of notes and a calculator are allowed.

Size: px

Start display at page:

Download "Record on a ScanTron, your choosen response for each question. You may write on this form. One page of notes and a calculator are allowed."

Egbert McCarthy
5 years ago
Views:

1 Ch 16, 17 Math 240 Exam 4 v1 Good SAMPLE No Book, Yes 1 Page Notes, Yes Calculator, 120 Minutes Dressler Record on a ScanTron, your choosen response for each question. You may write on this form. One page of notes and a calculator are allowed. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the expected value of the random variable. 1) x P(X = x) ) A) 8.7 B) 8.4 C) 7.5 D) 8.1 E) 6 2) The number of golf balls ordered by customers of a pro shop has the following probability distribution. x p(x) ) A) 7.74 B) 5.49 C) 9 D) 9.36 E)

2 Create a probability model for the random variable. 3) You roll a pair of fair dice. If you get a sum greater than 10 you win $80. If you get a double you win $20. If you get a double and a sum greater than 10 you win $100. Otherwise you win nothing. Create a probability model for the amount you win at this game. Amount won $0 $20 $80 $100 A) P(Amount won) Amount won $0 $20 $80 $100 B) P(Amount won) Amount won $0 $20 $80 $100 C) P(Amount won) Amount won $0 $20 $80 D) P(Amount won) Amount won $0 $20 $80 $100 E) P(Amount won) ) Find the expected value of the random variable. 4) A contractor is considering a sale that promises a profit of $36,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $6000 with a probability of 0.3. What is the expected profit? 4) A) $27,000 B) $23,400 C) $25,200 D) $30,000 E) $29,400 2

3 5) A company bids on two contracts. It anticipates a profit of $90,000 if it gets the larger contract and a profit of $10,000 if it gets the smaller contract. It estimates that thereʹs a 10% chance of winning the larger contract and a 70% chance of winning the smaller contract. Find the companyʹs expected profit. Assume that the contracts will be awarded independently. 5) A) $9000 B) $64,000 C) $23,000 D) $89,000 E) $16,000 Find the standard deviation of the random variable. Round to two decimal places if necessary. 6) x P(X = x) ) A) 2.71 B) 5.12 C) 3.32 D) 2.41 E)

4 Create a probability model for the random variable. 7) A company is interviewing applicants for managerial positions. They plan to hire two people. They have already rejected most candidates and are left with a group of 12 applicants of whom 4 are women. Unable to differentiate further between the applicants, they choose two people at random from this group of 12. Let the random variable X be the number of men that are chosen. Find the probability model for X. A) Number men P(Number men) B) Number men P(Number men) C) Number men P(Number men) D) Number men P(Number men) E) Number men P(Number men) ) Find the expected value of the random variable. 8) In a box of 10 batteries, 6 are dead. You choose two batteries at random from the box. Let the random variable X be the number of good batteries you get. Find the expected value of X. 8) A) µ = 0.80 B) µ = 1.00 C) µ = 0.53 D) µ = 0.75 E) µ =

5 Find the standard deviation of the random variable. 9) You have arranged to go camping for two days in March. You believe that the probability that it will rain on the first day is 0.4. If it rains on the first day, the probability that it also rains on the second day is 0.8. If it doesnʹt rain on the first day, the probability that it rains on the second day is 0.4. Let the random variable X be the number of rainy days during your camping trip. Find the standard deviation of X. 9) A) σ = 1.00 B) σ = 0.82 C) σ = 0.63 D) σ = 0.69 E) σ = 0.68 Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain. 10) We record the blood types (O, A, B, or AB) found in a group of 100 people. Assume that the people are unrelated to each other. 10) A) Yes. B) No, 400 is more than 10% of the population. C) No. More than two outcomes are possible. D) No.The chance of getting a particular blood group changes from one person to the next. E) No. The chance of getting a particular blood group depends on the blood groups already recorded. 5

6 Find the indicated probability. 11) A basketball player has made 78% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonightʹs game he misses for the first time on his 4th attempt? 11) A) B) C) D) E) ) Suppose that in a certain population 45% of people have type O blood. A researcher selects people at random from this population. What is the probability that there is a person with type O blood among the first 4 people checked? 12) A) B) C) D) E)

7 Solve. 13) An archer is able to hit the bullʹs eye 70% of the time. If she keeps shooting arrows until she hits the bullʹs-eye, how long do you expect it will take? Assume each shot is independent of the others. 13) A) 3.33 shots B) 0.70 shots C) 1.43 shots D) 70 shots E) 0.3 shots 14) A company finds that 58% of applicants for a job do not have the required qualifications. How many applications should they expect to read before finding a suitably qualified applicant? 14) A) 0.42 B) 1.72 C) 2.38 D) 0.58 E) 58 Find the indicated probability. 15) A multiple choice test has 6 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer none of the questions correctly? 15) A) B) C) D) E)

8 Find the probability of the outcome described. 16) A tennis player makes a successful first serve 65% of the time. If she serves 10 times, what is the probability that she gets no more than 3 first serves in? Assume that each serve is independent of the others. 16) A) B) C) D) E) Find the indicated probability. 17) Police estimate that 65% of drivers wear their seat belts. If they stop 5 drivers at random, whatʹs the probability that none of them are wearing their seat belts? 17) A) B) C) D) 0.35 E) ) A basketball player has made 70% of his foul shots during the season. If he shoots 5 foul shots in tonightʹs game, what is the probability that he doesnʹt make all of the shots? 18) A) B) C) 0.15 D) 0.3 E)

9 Solve the problem. 19) A company manufactures batteries in batches of 9 and there is a 3% rate of defects. Find the mean number of defects per batch. 19) A) B) 3.0 C) 0.27 D) 8.73 E) ) A company manufactures batteries in batches of 29 and there is a 3% rate of defects. Find the standard deviation of the number of defects per batch. 20) A) B) C) D) E) Describe an appropriate normal model that can be used to approximate the binomial distribution. If it is not appropriate to use a normal approximation, give a reason why not. 21) A laboratory worker finds that 2.6% of his blood samples test positive for the HIV virus. If 260 blood samples are selected at random, is it appropriate to use a normal model to approximate the distribution of the number that test positive for the HIV virus? 21) A) Yes; normal model with µ = 6.76 and σ = 2.57 can be used to approximate the distribution B) No; normal model cannot be used to approximate the distribution because nq < 10 C) Yes; normal model with µ = and σ = 2.57 can be used to approximate the distribution D) Yes; normal model with µ = 6.76 and σ = 6.58 can be used to approximate the distribution E) No; normal model cannot be used to approximate the distribution because np < 10 9

10 Find the indicated probability by using an appropriate normal model to approximate the binomial distribution 22) In one city, police estimate that 78% of drivers wear their seat belts. They set up a safety roadblock and they stop drivers to check for seat belt use. If 160 drivers are stopped, whatʹs the probability they find at least 30 not wearing their seat belts? 22) A) B) C) D) E) Use a Poisson model to find the indicated probability. 23) On one tropical island, hurricanes occur with a mean of 2.08 per year. Assuming that the number of hurricanes can be modeled by a Poisson distribution, find the probability that during the next 2 years the number of hurricanes will be 3. 23) A) B) C) D) E) ) The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 3.3. Find the probability that in a randomly selected year, the number of lightning strikes is 0. 24) A) B) C) D) E)

11 Describe the indicated sampling distribution model. 25) Assume that 32% of students at a university wear contact lenses. We randomly pick 500 students. Describe the sampling distribution model of the proportion of students in this group who wear contact lenses. 25) A) N(32%, 2.1%) B) N(68%, 2.1%) C) N(32%, 1.0%) D) There is not enough information to describe the distribution. E) Binom(500, 32) Provide an appropriate response. 26) An archer is usually able to hit the bullʹs-eye 75% of the time. He buys a new bow hoping that it will improve his success rate. During the first month of practice with his new bow he hits the bullʹs-eye 320 times out of 410 shots. Is this evidence that with the new bow his success rate has improved? In other words, is this an unusual result for him? Explain. 26) A) No; we would normally expect him to make bullʹs-eyes with a standard deviation of is 0.2 standard deviations above the expected value. Thatʹs not an unusual result. B) Yes; we would normally expect him to make bullʹs-eyes with a standard deviation of is 1.4 standard deviations above the expected value. Thatʹs an unusual result. C) No; we would normally expect him to make bullʹs-eyes with a standard deviation of is 0.7 standard deviations above the expected value. Thatʹs not an unusual result. D) Yes; we would normally expect him to make bullʹs-eyes with a standard deviation of is 0.2 standard deviations above the expected value. Thatʹs an unusual result. E) No; we would normally expect him to make bullʹs-eyes with a standard deviation of is 1.4 standard deviations above the expected value. Thatʹs not an unusual result. 11

12 27) A multiple choice test consists of 60 questions. Each question has 4 possible answers only one of which is correct. A student answers 26 questions correctly. Is that enough to convince you that he is not merely guessing? Explain. 27) A) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with a standard deviation of is 3.3 standard deviations above the expected value. That would be an unusual result. B) No; if the student were guessing, we would expect him to answer 15 questions correctly with a standard deviation of is 3.3 standard deviations above the expected value. That would not be an unusual result. C) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with a standard deviation of is 2.8 standard deviations above the expected value. That would be an unusual result D) Yes; if the student were guessing, we would expect him to answer 15 questions correctly with a standard deviation of is 3.5 standard deviations above the expected value. That would be an unusual result. E) No; if the student were guessing, we would expect him to answer 15 questions correctly with a standard deviation of is 0.98 standard deviations above the expected value. That would not be an unusual result Find the specified probability, from a table of Normal probabilities. 28) A candy company claims that its jelly bean mix contains 15% blue jelly beans. Suppose that the candies are packaged at random in small bags containing about 200 jelly beans. What is the probability that a bag will contain more than 11% blue jelly beans? 28) A) B) C) D) E)

13 Find the indicated probability by using an appropriate normal model to approximate the binomial distribution 29) An archer is able to hit the bullʹs eye 76% of the time. If she shoots 160 arrows in a competition, whatʹs the probability that she gets at least 130 bullʹs-eyes? Assume that shots are independent of each other. 29) A) B) C) D) E) ) A tennis player makes a successful first serve 65% of the time. If she serves 90 times in a match, whatʹs the probability that she makes no more than 50 first serves? Assume that each serve is independent of the others. 30) A) B) C) D) E) ) An airline, believing that 6% of passengers fail to show up for flights, overbooks. Suppose a plane will hold 320 passengers and the airline sells 335 seats. Whatʹs the probability the airline will not have enough seats and will have to bump someone? 31) A) B) C) D) E)

14 Answer Key Testname: EXAM4V3 CH 16,17 V1 GOOD SAMPLE WITHBINOMIAL 1) B 2) E 3) A 4) B 5) E 6) E 7) D 8) A 9) B 10) C 11) C 12) B 13) C 14) C 15) C 16) C 17) C 18) A 19) C 20) C 21) E 22) D 23) B 24) A 25) A 26) E 27) A 28) E 29) C 30) C 31) D 14

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Stats: Test Review - Chapters 16-17 Name Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the expected value of the random variable.