were selected at random, the probability that it is white or black would be 2 3.

Transcription

1 Math 1342 Ch, 4-6 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) What is the set of all possible outcomes of a probability experiment? A) events B) a Venn diagram C) an outcome D) the sample space 2) What type of probability uses a knowledge of sample spaces as opposed to experiments to determine the numerical probability that an event will occur? A) classical probability B) empirical probability C) conditional probability D) subjective probability 1) 2) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) If two dice are rolled one time, find the probability of getting a sum less than 5. 3) 4) A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are the same ("AA", "BB" or "CC"). [Hint: List all the outcomes of the sample space first.] 5) The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker? 6) A survey asked 32,011 homeowners how many pets they owned. The results were as followed: 4) 5) 6) Number of Pets Number of Homeowners , or more 800 Total 32,011 What is the probability that a sampled homeowner has three pets? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) A jar contains four white marbles, five red marbles, and six black marbles. If a marble 7) were selected at random, the probability that it is white or black would be 2 3. A) True B) False 1

2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 8) A single card is drawn from a deck. Find the probability of selecting a heart or a 8. 9) An apartment building has the following distribution of apartments: 1 bedroom 2 bedroom 3 bedroom 1st floor nd floor rd floor If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor? 10) If one card is drawn from an ordinary deck of cards, what is the probability that the card will be an ace, a king of hearts, or a spade? 11) In a recent semester at a local university, 500 students enrolled in both General Chemistry and Calculus I. Of these students, 66 received an A in general chemistry, 73 received an A in calculus, and 33 received an A in both general chemistry and calculus. 8) 9) 10) 11) Find the probability that a randomly chosen student received an A in general chemistry or calculus or both. 12) A poll was taken of 14,499 working adults aged to determine their level of education. The participants were classified by sex and by level of education. The results were as follows. 12) Education Level Male Female Total High School or Less Bachelor's Degree Master's Degree Ph.D Total ,499 A person is selected at random. Compute the probability that the person is female and has a bachelor's degree. 13) If P(A) = 0.38, P(B) = 0.33, and P(A and B) = 0.24, find P(A or B). 13) 14) If P(A) = 0.35, P(B) = 0.85, and P(A or B) = 0.86, are A and B mutually exclusive? 14) 2

3 15) Let A and B be events with P(A) = 0.7, P(B) = 0.3, and P(B A) = 0.2. Find P(A and B). 16) Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and B). 17) A fair die is rolled four times. What is the probability that it comes up 1 at least once? 18) A lot of 1000 components contains 150 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. 15) 16) 17) 18) Find P(A). 19) According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 4 adults at random. The probability that all of them enjoy drinking beer is: 20) In a second grade class containing 12 girls and 11 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls? 21) Urn 1 contains 3 red balls and 4 black balls. Urn 2 contains 4 red balls and 2 black balls. Urn 3 contains 6 red balls and 5 black balls. If an urn is selected at random and a ball is drawn, find the probability it will be red. 22) It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph? 23) There are 3 blue balls, 5 red balls, and 2 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white? 24) A box contains blue chips and red chips. A person selects two chips without 19) 20) 21) 22) 23) 24) replacement. If the probability of selecting a blue chip and a red chip is 1 4, and the probability of selecting a blue chip on the first draw is 5, find the 16 probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip. 25) A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done? 25) 3

4 26) There are 3 different mathematics courses, 3 different science courses, and 5 different history courses. If a student must take one of each, how many different ways can this be done? 27) How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together? 28) Three statistics professors and seven chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advisors. If each professor has an equal chance of being selected, what is the probability that both professors are chemistry professors? 29) If 20 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets. 30) If five cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a heart? 31) A committee consist of 8 women and 11 men. Three members are chosen as officers. What is the probability that all three officers are women? 26) 27) 28) 29) 30) 31) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 32) The sum of the probabilities of all the events in the sample space of a probability distribution must equal 1. A) True B) False 33) The following distribution is not a probability distribution because X P(X) A) the probability values are not increasing. B) the probability values are not discrete. C) the values of the variable are negative. D) the probability values do not add to 1. 34) Which of the following variables are continuous? i. an automobile's gas mileage ii. the air pressure in an automobile's spare tire iii. an automobile's sticker price A) i and ii B) i, ii, and iii C) i D) None are continuous. 32) 33) 34) 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 35) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find the probability that a family took at least 3 vacations last year. 35) x P(x) ) What is the standard deviation of the following probability distribution? 36) X P(X) ) Give the mean of the following probability distribution. 37) X P(X) ) The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the standard deviation σ. 38) x P(x) ) Compute the standard deviation of the random variable with the given discrete probability distribution. 39) x P(x) ) If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game? 40) 5

6 41) Compute the probability of X successes. n = 5, X = 4, p = ) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n =12, p = 0.7, P(3 or fewer) 43) It is estimated that 25% of households own a riding lawn mower. A sample of 16 households is studied. What is the probability that exactly 5 of these own a riding lawn mower? 44) A student takes a 18-question, multiple-choice exam with four choices for each question and guesses on each question. Find the probability of guessing exactly 7 out of 18 correctly. 45) Find the variance for the values of n and p when the conditions for the binomial distribution are met. n = 500, p = ) A university has 10,000 students of which 35% are male and 65% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students. 47) A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers. 48) Use the multinomial formula and find the probability for the following data. n =6, X 1 = 3, X 2 = 2, X 3 = 1, p 1 = 0.58, p 2 = 0.25, p 3 = ) If there are 20 typographical errors randomly distributed in a 250-page document, find the probability that a given page contains exactly two errors. 41) 42) 43) 44) 45) 46) 47) 48) 49) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 50) In the instructor's answer book for a mathematics text, 8% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2 incorrect answers for a homework set with 50 problems. A) e B) e C) e D) e ! 4! 2! 8! 50) 6

7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 51) In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones. 52) The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find P(Greater than 1). 53) For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probability of approximately 68%? 51) 52) 53) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 54) Which of the following properties distinguishes the standard normal distribution from other normal distributions? A) The curve is continuous. B) The mean is located at the center of the distribution. C) The mean is 0 and the standard deviation is 1. D) The total area under the curve is equal to ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 55) Find the area under the standard normal distribution curve between z = 0 and z = ) 7

8 56) What is the area under the standard normal distribution curve between z = 1.50 and z = 2.50? 56) 57) Find the probability P(0 < z < 1.67), using the standard normal distribution. 57) 58) Find the z value that corresponds to the given area. 58) 59) If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below ) The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is more than 11 feet long. 59) 60) 8

9 61) X is a normally distributed random variable with a mean of If the probability that X is less than is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.) 61) 62) X is a normally distributed random variable with a standard deviation of Find the mean of X if 12.71% of the area under the distribution curve lies to the right of (Note: the diagram is not necessarily to scale.) 62) 63) For a normal distribution with a mean of 13 and a standard deviation of 6, the value 1 has a z value of 63) 64) A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that x will be less than ) A ferry will safely accommodate 91 tons of passenger cars. Assume that the mean weight of a passenger car is 2.1 tons with standard deviation 0.7 tons. If a random sample of 40 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded? 66) Use the normal approximation to the binomial to find that probability for the specific value of X. n = 30, p = 0.4, X = 5 64) 65) 66) 9

10 67) Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 78, p = 0.59: P(X > 42) 68) A gardener buys a package of seeds. Seventy-six percent of seeds of this type germinate. The gardener plants 110 seeds. Approximate the probability that fewer than 77 seeds germinate. 69) A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have this tick? 70) A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving. 67) 68) 69) 70) 10

11 Answer Key Testname: MATH1342 CH. 4,5,6 REVIEW 1) D 2) A 3) 1 6 4) 1/3 5) 5 8 6) ) A 8) ) ) ) ) ) ) No 15) ) ) ) ) ) ) ) ) ) ) 24 26) 45 27) 12 28)

12 Answer Key Testname: MATH1342 CH. 4,5,6 REVIEW 29) ) ) ) A 33) D 34) A 35) ) ) ) ) ) $ ) ) ) ) ) ) Mean = 10.5, Variance = ) Mean = 6.7, Variance = ) ) ) C 51) ) ) from 10 to 20 54) C 55) ) ) 45.25% 58) ) 4.75% 60) ) ) ) -2 64) ) ) ) )

13 Answer Key Testname: MATH1342 CH. 4,5,6 REVIEW 69) ) 1.3% 13