MATH 210
Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 12.5, and the standard deviation is 0.58. Would it be unusual to randomly select 15 people and find that fewer than 9 recognize the Yummy brand name? a. yes b. no
a. yes
A test subject is randomly selected and tested for the disease. What is the probability the subject does not have the disease given that the test result is positive? a. 0.225 b. 0.775 c. 0.141 d. 0.65
a. 0.225
A bin contains 64 light bulbs of which 10 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. 0.428 b. 0.844 c. 0.484 d. 0
a. 0.428
Of the 64 people who answered "yes" to a question, 6 were male. Of the 70 people that answered "no" to the question, 8 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? a. 0.537 b. 0.104 c. 0.094 d. 0.582
a. 0.537
100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the person drives alone or cycles to work. 1. Public transportation: 10 full time, 10 part time 2. Bicycle: 3 full time, 3 part time 3. Drive alone: 31 full time, 26 part time 4. Carpool: 9 full time, 8 part time a. 0.63 b. 0.60 c. 0.57 d. 0.34
a. 0.63
A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 40 that have no defects. What is the probability that at least one of the calculators is defective? a. 0.785 b. 0.180 c. 0.774 d. 0.215
a. 0.785
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 1665; p = 0.57 a. u = 949.1 b. u = 958.8 c. u = 941.6 d. u = 956.4
a. u = 949.1
A tennis player makes a successful first serve 51% 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. 0.154 b. 0.133 c. 0.00184 d. 0.0635
a. 0.154
Of ten adults, at least one of them has high blood pressure. a. None of the adults have high blood pressure b. All of the adults have high blood pressure c. At most one of the adults has high blood pressure d. Nine of the adults have high blood pressure
a. None of the adults have high blood pressure
Assume that there is a 0.15 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. no b. yes
a. no
Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 or a 3, nothing otherwise. What is your expected value? a. $4.00 b. -$0.67 c. -$2.00 d. $2.00
b. -$0.67
In a game, you have a 1/36 probability of winning and a 35/36 probability of losing What is your expected value? a. -$3.89 b. -$1.53 c. $6.25 d. $2.36
b. -$1.53
A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? a. $149,910.00 b. -$91.00 c. $90.00 d. -$180.89
b. -$91.00
Among the contestants in a competition are 46 women and 23 men. If 5 winners are randomly selected, what is the probability that they are all men? Round to five decimal places. a. 0.03125 b. 0.00299 c. 0.02455 d. 0.13169
b. 0.00299
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. n = 30, x = 12, p = 0.20 a. 0.014 b. 0.006 c. 0.003 d. 0.108
b. 0.006
An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least one correct answer. a. 0.100 b. 0.999 c. 0.900 d. 0.001
b. 0.999
An insurance company in the town of Codrington sells life insurance. They are determining the premium for a $100,000 life insurance for a 50-year old woman. The probability that a 50-year old woman in Codrington survives the year is 0.9963. The company sells 1200 such policies to 50-year old females. The company will use the Poisson distribution to approximate the probability of various number of deaths during the year in this group of 1200 women. Find the mean of the appropriate Poisson distribution (the mean number of deaths in a year in such groups of 1200 females). Round your answer to the nearest hundredth. a. 0.44 b. 4.44 c. 44.4 d. 1195.56
b. 4.44
A die with 12 sides is rolled. What is the probability of rolling a number less than 11? a. 1/12 b. 5/6 c. 11/12 d. 10
b. 5/6, there are 10 numbers less than 11,so the probability is 10/12 which reduces to 5/6
10P3 a. 120 b. 720 c. 7 d. 27
b. 720
Which of the following cannot be a probability? a. 1 b. 1/2 c. -1 d. 0
c. -1, a probability is a value between 0 & 1.
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting 12 or more girls. a. 0.006 b. 0.001 c. 0.007 d. 0.022
c. 0.007
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting exactly 4 girls. a. 0.001 b. 0.022 c. 0.061 d. 0.122
c. 0.061
In one town, 44% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary. a. 0.440 b. 0.189 c. 0.194 d. 0.880
c. 0.194
In the town of Maplewood a certain type of DVD player is sold at just two stores. 43% of the sales are from store A and 57% of the sales are from store B. 2.4% of the DVD players sold at store A are defective while 4.0% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? a. 0.024 b. 0.453 c. 0.312 d. 0.688
c. 0.312
3! a. 3 b. 2 c. 6 d. 9
c. 6
Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50% a. NNN RNN NR b. NR NNR NNR c. NNR NNN d. N NN NR NNN NRN
c. NNR NNN
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. n = 4, x = 3, p = 1/6 a. 0.004 b. 0.012 c. 0.023 d. 0.015
d. 0.015
A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.9. Find the probability that on a randomly selected trip, the number of whales seen is 5. a. 0.0525 b. 0.7407 c. 0.1543 d. 0.0309
d. 0.0309
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. 5.8 b. 18 c. 1.8 d. 0.2
d. 0.2
A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? a. 0.828 b. 0.172 c. 0.205 d. 0.377
d. 0.377
How many ways can an IRS auditor select 3 of 9 tax returns for an audit? a. 6 b. 504 c. 729 d. 84
d. 84
When several textbooks are edited, none of them are found to be free of errors. a. One of the textbooks is free of errors b. At most one of the textbooks is free of errors c. All of the textbooks are free of errors d. At least one of the textbooks is free of errors
d. At least one of the textbooks is free of errors
Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene dominates. List the possible outcomes. a. WW, BB b. WB, BW c. WW, WW d. WW, BW
d. WW, BW
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 503; p = 0.7 a. o = 14.40 b. o = 13.55 c. o = 7.87 d. o = 10.28
d. o = 10.28
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 676; p = 0.7 a. u = 471.7 b. u = 474.9 c. u = 474.5 d. u = 473.2
d. u = 473.2
5P4 a. 1 b. 5 c. 24 d. 120
d. 120
Suppose the probability of a major earthquake on a given day is 1 out of 11,000. Use the Poisson distribution to approximate the probability that there will be at least one major earthquake in the next 2000 days. a. 0.1662 b. 0.8338 c. 0.1516 d. 0.0147 e. 0.8484
a. 0.1662
A company manufactures batteries in batches of 15 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch. a. 0.8 b. 43.7 c. 0.4 d. 0.2
a. 0.7
There are 8 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? a. 28 b. 20160 c. 262144 d. 720
a. 28
One of the 100 test subjects is selected at random. Given that the person selected approves of the mayor, what is the probability that they vote Democrat? a. 0.581 b. 0.674 c. 0.545 d. 0.391
c. 0.545
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction. a. 25/51 b. 13/51 c. 1/2652 d. 25/102
d. 25/102
Determine whether the events are disjoint. Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass. Yes No
No, you can find a dollar bill on the sidewalk and the grass
Determine whether the events are disjoint. Draw one ball colored red from a bag. Draw one ball color blue from the same bag. Yes No
Yes, the ball can't be both blue and red
A multiple choice question has 18 possible answers, only one of which is correct. Is it unlikely to answer a question correctly if a random guess is made? Yes No
Yes, the chance is 1/18 = 0.05
Assume that a study of 500 randomly selected school bus routes showed that 482 arrived on time. Is it unlikely for a school bus to arrive late? Yes No
Yes, the school buses that arrive late are 18/500 = 0.36
Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. Is it unlikely to get a 12 when a pair of dice is rolled? Yes No
Yes, there is one way (6, 6) out of 36 combinations. 0.028
Determine whether the events are disjoint. Get a full time day job as a teller with a bank. Get a full time day job as a cashier at a store. Yes No
Yes, you can't have two full time day jobs
In a survey of 300 college graduates, 56% reported that they entered a profession closely related to their college major. If 8 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major? a. 0.162 b. 0.0637 c. 0.176 d. 0.838
a. 0.162
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 11,000 cars passing through this tunnel, at most two will have a flat tire. a. 0.9898 b. 0.9377 c. 0.9274 d. 0.0623 e. 0.0726
a. 0.9898
On a multiple choice test with 17 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. a. 4.3 b. 8.5 c. 5.7 d. 12.8
a. 4.3
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time. a. 76/87 b. None of the above is correct. c. 43/87 d. 11/76
a. 76/87
Rolling a single die 53 times, keeping track of the "fives" rolled. a. Procedure results in a binomial distribution b. Not binomial: there are too many trials c. Not binomial: there are more than two outcomes for each trial d. Not binomial: the trials are not independent
a. Procedure results in a binomial distribution
Find the mean of the given probability distribution. The number of golf balls ordered by customers of a pro shop has the following probability distribution. x P(x) 3 0.14 6 0.29 9 0.36 12 0.11 15 0.10 a. u = 8.22 b. u = 5.55 c. u = 9 d. u = 9.3
a. u = 8.22
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 - 2σ or greater than μ + 2σ. 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. no b. yes
b. yes
Use the Poisson Distribution to find the indicated probability.If the random variable x has a Poisson Distribution with mean u = 3, find the probability that x = 5. a. 0.01680 b. 0.10082 c. 0.12602 d. 0.27405
b. 0.10082
The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will have a flat tire. a. 0.1947 b. 0.1217 c. 0.1703 d. 0.1460 e. 0.8783
b. 0.1217
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Find the probability of selecting exactly 8 girls. a. 0.122 b. 0.183 c. 0.000 d. 0.022
b. 0.183
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. n = 10, x = 2, p = 1/3 a. 0.003 b. 0.195 c. 0.216 d. 0.193
b. 0.195
A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. a. 0.429 b. 0.343 c. 0.027 d. 2.1
b. 0.343
Based on the meteorological records, the probability that it will snow in a certain town on January 1st is 0.428. Find the probability that in a given year it will not snow on January 1st in that town. a. 0.748 b. 0.572 c. 2.336 d. 1.428
b. 0.572, 1-0.428
A mountain search and rescue team receives a mean of 0.78 calls per day. Find the probability that on a randomly selected day, they will receive fewer than two calls. a. 0.1840 b. 0.8160 c. 0.3576 d. 0.1394
b. 0.8160
Two 6-side dice are rolled. What is the probability that the sum of the two numbers on the dice will be 3? a. 17/18 b. 1/18 c. 1/2 d. 2
b. 1/18, this can happen two ways: (1, 2) or (2,1). There are 36 total combinations. So, P( Sum is 3)= 2/36 or 1/18.
A 6-sided die is rolled. Find P(3 or 5). a. 1/6 b. 1/3 c. 2 d. 1/36
b. 1/3
On a multiple choice test with 29 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers. a. 29.6 b. 2.3 c. 5.4 d. 54.4
b. 2.3
According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. a. 0.2 b. 3.5 c. 4.0 d. 2.8
b. 3.5
From the information provided, create the sample space of possible outcomes. Flip a coin twice. a. HH HT TT b. HH HT TH TT c. HT TH d. HH TT HT HT
b. HH HT TH TT, shows every possible outcome
Choosing 5 people (without replacement) from a group of 40 people, of which 15 are women, keeping track of the number of men chosen. a. Not binomial: there are more than two outcomes for each trial b. Not binomial: the trials are not independent. c. Procedure results in a binomial distribution d. Not binomial: there are too many trials
b. Not binomial: the trials are not independent
The pH level in a shampoo a. discrete b. continuous
b. continuous
The cost of a randomly selected orange a. continuous b. discrete
b. discrete
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 530 consumers who recognize the Dull Computer Company name? a. yes b. no
b. no
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 0.111 1 0.215 2 0.450 3 0.224 a. yes b. no
b. no
In a certain town, 70% 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. Find the standard deviation for the probability distribution. x P(x) 0 0.0081 1 0.0756 2 0.2646 3 0.4116 4 0.2401 a. o = 0.84 b. o = 0.92 c. o = 1.06 d. o = 2.95
b. o = 0.92
Find the standard deviation for the given probability distribution. x P(x) 0 0.37 1 0.13 2 0.06 3 0.15 4 0.29 a. o = 2.52 b. o = 1.70 c. o = 1.81 d. o = 2.90
b. o = 1.70
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n = 38; p = 0.2 a. u = 7.1 b. u = 7.6 c. u = 7.9 d. u = 8.3
b. u = 7.6
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 981 of the 2500 televisions are tuned to "Eyewitness News"? a. no b. yes
b. yes
The mean number of homicides per year in one city is 21.4. 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. 21.4 b. 5.35 c. 0.0586 d. 0.412
c. 0.0586
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. 0.196 b. 0.279 c. 0.649 d. 0.535
c. 0.649
According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16. a. 3.5 b. 1.9 c. 1.7 d. 2.6
c. 1.7
8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected? a. 8/27 b. 1/40320 c. 1/2220075 d. 1/213127200
c. 1/2220075
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age. a. 3/5 b. 1/2 c. 1/3 d. 2/5
c. 1/3
There are 6 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? a. 720 b. 20 c. 120 d. 216
c. 120
A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? a. 7/9 b. 12 c. 2/3 d. 1/3
c. 2/3, even numbers 1-15 = 2, 4, 6, 8, 10, 12, 14. multiples of 3 1-15 = 3, 6, 9, 12, 15. 6, 12 are both even and multiples of 3. 7+5=12. 12-2=10. 10/15=2/3
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age given that they drink root beer. a. 5/17 b. None of the above is correct c. 2/5 d. 6/27
c. 2/5
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed? a. 5 b. 343 c. 210 d. 6
c. 210
A musician plans to perform 8 selections. In how many ways can she arrange the musical selections? a. 64 b. 362880 c. 40320 d. 8
c. 40320
Rolling a single die 26 times, keeping track of the numbers that are rolled. a. Not binomial: the trials are not independent. b. Not binomial: there are too many risks c. Not binomial: there are more than two outcomes for each trial d. Procedures results in a binomial distribution
c. Not binomial: there are more than two outcomes for each trial
Find the mean of the given probability distribution. x P(x) 0 0.26 1 0.11 2 0.16 3 0.05 4 0.42 a. u = 2.16 b. u = 2.42 c. u = 2.26 d. u = 2.52
c. u = 2.26
The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name. a. 0.0448 b. 0.00381 c. 0.250 d. 0.267
d. 0.267
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 0.1, what is the probability that the mixture will test positive? a. 0.531 b. 1.00 c. 0.00000100 d. 0.469
d. 0.469
If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker. a. 0.557 b. 0.596 c. 0.511 d. 0.554
d. 0.554
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority? a. 0.985 b. 0.913 c. 0.055 d. 0.982
d. 0.982
What is the probability that 4 randomly selected people all have different birthdays? Round to four decimal places. a. 0.9891 b. 0.9918 c. 0.9729 d. 0.9836
d. 0.9836
What is the probability of an event that is certain to occur? a. 0.95 b. 0.5 c. 0.99 d. 1
d. 1, 1 is certain and 0 is impossible
If P(A) = 14/15, find the complement of P(A). a. 0 b. 15/14 c. 14/29 d. 1/15
d. 1/15, the complement is the events that are unlikely to happen
A sample space consists of 38 separate events that are equally likely. What is the probability of each? a. 38 b. 1 c. 0 d. 1/38
d. 1/38, they are all equally likely, so they all have a 1/38 chance of happening
On a multiple choice test with four possibilities for each question, what is the probability of answering a question correctly if you make a random guess? a. 3/4 b. 1/2 c. 1 d. 1/4
d. 1/4, you have a one if four chance of getting the answer correctly, and a 3 in four chance of getting it wrong
If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. a. 31/365 b. 31/334 c. 11/12 d. 334/365
d. 334/365, there are 31 days in May, 365-31=334
A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4). a. 2/13 b. 12/13 c. 16 d. 4/13
d. 4/13
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 29; p = 0.2 a. o = 6.27 b. o = 5.42 c. o = -0.026 d. o = 2.15
d. o = 2.15
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 1680; p = 0.57 a. o = 17.88 b. o = 24.41 c. o = 23.56 d. 0 = 20.29
d. o = 20.29
