Introduction to Management Science, 10e (Taylor) Chapter 11 Probability and Statistics




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Introduction to Management Science, 10e (Taylor)

Chapter 11 Probability and Statistics


1) Deterministic techniques assume that no uncertainty exists in model parameters.

Answer: TRUE

Diff: 1 Page Ref: 489

Main Heading: Types of Probability

Key words: deterministic techniques


2) Probabilistic techniques assume that no uncertainty exists in model parameters.

Answer: FALSE

Diff: 1 Page Ref: 489

Main Heading: Types of Probability

Key words: probabilistic techniques


3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori.

Answer: TRUE

Diff: 2 Page Ref: 489

Main Heading: Types of Probability

Key words: objective probabilities, classical probabilities


4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies.

Answer: TRUE

Diff: 2 Page Ref: 489

Main Heading: Types of Probability

Key words: relative frequencies


5) Relative frequency is the more widely used definition of objective probability.

Answer: TRUE

Diff: 1 Page Ref: 490

Main Heading: Types of Probability

Key words: relative frequencies


6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation.

Answer: TRUE

Diff: 2 Page Ref: 490

Main Heading: Types of Probability

Key words: subjective probability


7) An experiment is an activity that results in one of several possible outcomes.

Answer: TRUE

Diff: 1 Page Ref: 491

Main Heading: Fundamentals of Probability

Key words: experiment


8) The events in an experiment are mutually exclusive if only one can occur at a time.

Answer: TRUE

Diff: 1 Page Ref: 491

Main Heading: Fundamentals of Probability

Key words: mutually exclusive events

9) In a given experiment, the probabilities of all mutually exclusive events sum to one.

Answer: TRUE

Diff: 1 Page Ref: 491

Main Heading: Fundamentals of Probability

Key words: mutually exclusive events, rules of probability


10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment.

Answer: TRUE

Diff: 2 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: collectively exhaustive events


11) A marginal probability is the probability of a single event occurring.

Answer: TRUE

Diff: 1 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: marginal probability


12) A Venn diagram visually displays mutually exclusive and non-mutually exclusive events.

Answer: TRUE

Diff: 2 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: Venn diagram


13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.

Answer: FALSE

Diff: 2 Page Ref: 493

Main Heading: Fundamentals of Probability

Key words: joint probability


14) A conditional probability is the probability that an event occurs given that another event has already occurred.

Answer: TRUE

Diff: 1 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: conditional probability


15) Conditional probabilities are shown in Venn diagrams.

Answer: FALSE

Diff: 1 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: conditional probability


16) Probability trees are used only to compute conditional probabilities.

Answer: FALSE

Diff: 2 Page Ref: 496

Main Heading: Fundamentals of Probability

Key words: probability tree, conditional probability

17) A succession of events that does not affect other events is independent.

Answer: TRUE

Diff: 1 Page Ref: 495

Main Heading: Statistical Independence and Dependence

Key words: independence


18) A binomial probability distribution indicates the probability of r successes in n trials.

Answer: TRUE

Diff: 2 Page Ref: 497

Main Heading: Statistical Independence and Dependence

Key words: binomial probability distribution


19) The chi-square test is a statistical test to determine if data that are squared exhibit bias.

Answer: TRUE

Diff: 1 Page Ref: 511

Main Heading: The Normal Distribution

Key words: chi-square test


20) A continuous random variable may assume only integer values within a given interval.

Answer: FALSE

Diff: 1 Page Ref: 504

Main Heading: The Normal Distribution

Key words: continuous random variables


21) Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

Answer: FALSE

Diff: 1 Page Ref: 504

Main Heading: The Normal Distribution

Key words: normal distribution


22) Another name for the mean of a probability distribution is its expected value.

Answer: TRUE

Diff: 1 Page Ref: 503

Main Heading: Mean

Key words: mean of probability distribution; expected value


23) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736.

Answer: TRUE

Diff: 2 Page Ref: 497

Main Heading: Statistical Independence and Dependence

Key words: binomial probability distribution


24) In Bayesian analysis, additional information is used to alter the conditional probability of the occurrence of an event.

Answer: FALSE

Diff: 1 Page Ref: 495

Main Heading: Bayesian Analysis

Key words: conditional probability

25) Objective probabilities that can be stated prior to the occurrence of an event are __________.

Answer: classical or a priori

Diff: 1 Page Ref: 489

Main Heading: Types of Probability

Key words: probabilistic techniques, objective/classical probabilities


26) __________ probability is an estimate based on a personal belief, experience, and knowledge of a situation.

Answer: Subjective

Diff: 1 Page Ref: 490

Main Heading: Types of Probability

Key words: subjective probability


27) The events in an experiment are __________ if only one can occur at a time.

Answer: mutually exclusive

Diff: 1 Page Ref: 491

Main Heading: Fundamentals of Probability

Key words: mutually exclusive events


28) A __________ organizes numerical data to describe the events of an experiment.

Answer: frequency distribution

Diff: 1 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: frequency distribution


29) A __________ is the probability of occurrence of a single event.

Answer: marginal probability

Diff: 1 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: marginal probability


30) __________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information.

Answer: Bayesian analysis

Diff: 2 Page Ref: 501

Main Heading: Fundamentals of Probability

Key words: Bayesian analysis


31) A succession of events that do not affect each other are __________.

Answer: independent

Diff: 2 Page Ref: 495

Main Heading: Statistical Independence and Dependence

Key words: independence


32) A __________ probability is the probability that an event will occur given that another event has already occurred.

Answer: conditional

Diff: 2 Page Ref: 495

Main Heading: Statistical Independence and Dependence

Key words: conditional probability

33) In a binomial distribution process, there are __________ possible outcomes.

Answer: two

Diff: 2 Page Ref: 497

Main Heading: Statistical Independence and Dependence

Key words: binomial distribution


34) One of the properties of the __________ distribution is that the probability of success remains constant over time.

Answer: binomial

Diff: 2 Page Ref: 497

Main Heading: Statistical Independence and Dependence

Key words: binomial distribution


35) Altered marginal probability of an event based on additional information is a __________ probability.

Answer: posterior

Diff: 2 Page Ref: 501

Main Heading: Statistical Independence and Dependence

Key words: Bayesian analysis, posterior probability


36) The __________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products.

Answer: expected value

Diff: 1 Page Ref: 503

Main Heading: Statistical Independence and Dependence

Key words: random variables, expected value


37) If events A and B are independent, then P(AB) = __________.

Answer: P(A) ∙ P(B)

Diff: 1 Page Ref: 495

Main Heading: Probability

Key words: probabilistic techniques, objective/classical probabilities


38) If events A and B are independent, then P(A|B) = __________.

Answer: P(A)

Diff: 1 Page Ref: 495

Main Heading: Probability

Key words: probabilistic techniques, objective/classical probabilities


39) If two events are not mutually exclusive, then P(A or B) = __________.

Answer: P(A) + P(B) - P(AB)

Diff: 1 Page Ref: 495

Main Heading: Probability

Key words: probabilistic techniques, objective/classical probabilities


40) __________ is a measure of dispersion of random variable values about the expected value.

Answer: Variance

Diff: 1 Page Ref: 503

Main Heading: Statistical Independence and Dependence

Key words: random variables, variance

41) A continuous random variable can take on a(n) __________ number of values within a given interval.

Answer: infinite

Diff: 2 Page Ref: 504

Main Heading: The Normal Distribution

Key words: continuous random variables


42) The __________ test is a statistical test to see if an observed data fit a particular probability distribution.

Answer: chi-square

Diff: 2 Page Ref: 511

Main Heading: The Normal Distribution

Key words: chi-square test


43) The __________ normal distribution has a mean of 0 and a standard deviation of 1.

Answer: standard

Diff: 2 Page Ref: 504

Main Heading: The Normal Distribution

Key words: standard normal distribution


44) Almost all of the data from a normal distribution fall within __________ standard deviations of the mean.

Answer: 3

Diff: 1 Page Ref: 504

Main Heading: The Normal Distribution

Key words: standard normal distribution


45) The expected value of the standard normal distribution is equal to __________.

Answer: 0

Diff: 1 Page Ref: 504

Main Heading: The Normal Distribution

Key words: expected value, standard normal distribution


46) The standard deviation of the standard normal distribution is equal to __________.

Answer: 1

Diff: 1 Page Ref: 504

Main Heading: The Normal Distribution

Key words: expected value, standard normal distribution


Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y.


47) What is the probability that Jim will be accepted at both universities?

Answer: 0.09

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: multiplication of probabilities

48) What is the probability that Jim will not be accepted at either university?

Answer: 0.44 = (.55) x (.80)

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: multiplication of probabilities


49) What is the probability that Jim will be accepted by at least one of the two universities?

Answer: 0.56 =1- [(.55) x (.80)]

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: multiplication of probabilities


Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.


Male (M) Female (F)

Job

Administrative (AD) 110 10

Salaried staff (SS) 30 50

Hourly staff (HS) 60 40


50) If an employee is selected at random, what is the probability that the employee is male?

Answer: .667 = 200/300

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: marginal probability


51) If an employee is selected at random, what is the probability that the employee is male and salaried staff?

Answer: .10 = 30/300

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: joint probability


52) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member?

Answer: .625 = 50/80

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: conditional probability


53) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration

Answer: .70 = 100/300 + 120/300 -10/300

Diff: 2 Page Ref: 495

Main Heading: Fundamentals of Probability

Key words: not mutually exclusive events, addition rule

An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.


xi

0

1

2

3

4

5

6

p(xi)

.10

.15

.18

.20

.20

.10

.07


54) What is the probability that they receive less than 3 complaints in a week?

Answer: 0.43

Diff: 2 Page Ref: 492

Main Heading: Fundamentals of Probability

Key words: probability distribution


55) What is the average number of complaints received per week?

Answer: 2.83

Diff: 2 Page Ref: 503

Main Heading: Expected Value

Key words: expected value, probability distribution


56) A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times?

Answer: 0.0899

Diff: 2 Page Ref: 495

Main Heading: The Binomial Distribution

Key words: binomial distribution


57) A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times?

Answer: 0.6016

Diff: 2 Page Ref: 495

Main Heading: The Binomial Distribution

Key words: binomial distribution


A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of "success" is 80%. Assume that the probability of success is independent for each product.


58) Find the probability that exactly 1 of the 3 products is successful.

Answer: (3)(.8)(.2)(.2) = .096

Diff: 2 Page Ref: 497

Main Heading: The Binomial Distribution

Key words: binomial distribution


59) Find the probability that none of the 3 products is successful.

Answer: (1)(.2)(.2)(.2) = .008

Diff: 2 Page Ref: 497

Main Heading: The Binomial Distribution

Key words: binomial distribution

60) If X has the following probability distribution


X 1 2 3 4

P(X) .1 .5 .2 .2


Compute the expected value of X

Answer: 2.5 EV = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) =2.5

Diff: 2 Page Ref: 503

Main Heading: Expected Value

Key words: expected value


61) If X has the following probability distribution


X 1 2 3 4

P(X) .1 .5 .2 .2


Compute the standard deviation of X.

Answer: .95524

Diff: 2 Page Ref: 503

Main Heading: Expected Value

Key words: standard deviation


62) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ __)?

Answer: -4/3

Diff: 3 Page Ref: 506

Main Heading: The Normal Distribution

Key words: normal distribution


63) For a standard normal distribution, what is the probability that z is greater than 1.75?

Answer: 0.0401

Diff: 3 Page Ref: 506

Main Heading: The Normal Distribution

Key words: normal distribution


Two Psychology majors, in 2 different sections of Clinical Psychology, were comparing test scores. The following gives the students' scores, class mean, and standard deviation for each section:


Section 1 Section 2

Student Score 84 75

Mean 75 60

Standard deviation 7 8


64) What is the z-score of the student from section 1 and what is the probability that a student in section 1 will score higher than 84?

Answer: 1.286 and .0985

Diff: 3 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: normal distribution

65) What is the z-score of the student from section 2 and what is the probability that a student in section 2 will score higher than 75?

Answer: 1.875 and .0301

Diff: 3 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


66) Which student scored better compared to the rest of the section?

Answer: section 2 student because their z-score is higher

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: mean, standard deviation


67) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?

Answer: 0.9772

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


68) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz?

Answer: 0.0228

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


69) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz?

Answer: 1

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


70) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz?

Answer: 0.9876

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


71) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz?

Answer: 0.3830

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution

72) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz?

Answer: 0

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


73) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz?

Answer: 0.3085

Diff: 2 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: norm distrib, probability calculations with normal distribution


74) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75?

Answer: 0.0401

Diff: 1 Page Ref: 506-509

Main Heading: Normal Distribution, Probability

Key words: norm distrib, probability calculations with normal distribution


75) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65?

Answer: 0.2266

Diff: 2 Page Ref: 506-509

Main Heading: Normal Distribution, Probability

Key words: norm distrib, probability calculations with normal distribution


76) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants pass away?

Answer: 71.36 years old

Diff: 3 Page Ref: 506-509

Main Heading: Normal Distribution, Value

Key words: norm distrib, probability calculations with normal distribution


77) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations?

Answer: 95%

Diff: 1 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: normal distribution


78) What is the area under the normal curve for ≥ 1.79?

Answer: 0.0367

Diff: 3 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: normal distribution

79) A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt?

Answer: 15.87%

Diff: 3 Page Ref: 506-509

Main Heading: The Normal Distribution

Key words: normal distribution


80) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crab are normally distributed, what is the probability that a randomly selected crab will weigh more than 2 .2 pounds?

Answer: 0.0668

Diff: 1 Page Ref: 506-509

Main Heading: Normal Distribution, Probability

Key words: norm distrib, probability calculations with normal distribution


81) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds?

Answer: 0.7745

Diff: 1 Page Ref: 506-509

Main Heading: Normal Distribution, Probability

Key words: norm distrib, probability calculations with normal distribution


82) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is __________.

Answer: 0.1587

Diff: 1 Page Ref: 506-509

Main Heading: Normal Distribution, Probability

Key words: norm distrib, probability calculations with normal distribution


83) Assume that
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