Free Printable SB - Chapter 6

1.

If X is a discrete uniform random variable ranging from 0 to 12, find P(X ≥ 10).

a)

.1126

b)

.2500

c)

.2308

d)

.1666

2.

If X is a discrete uniform random variable ranging from one to eight, find P(X < 6).

a)

.6250

b)

.7500

c)

.3750

d)

.5000

3.

Which of the following characterizes a Bernoulli process?

a)

A random experiment that has only two outcomes.

b)

The "success" must be a desirable outcome.

c)

.Either outcome has the same chance of occurrence.

d)

The probability of "success" varies with each trial.

4.

The expected value (mean) of a binomial variable is 25. The number of trials is 50. The probability of "success" is:

a)

.75

b)

.50

c)

.30

d)

.25

5.

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

a)

.8131

b)

.3826

c)

.6174

d)

.1869

6.

If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

a)

.0116

b)

.3151

c)

.1872

d)

.5987

7.

Based on experience, 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant. In a random sample of 12 women, what is the probability that at least 10 are pregnant?

a)

.0835

b)

.1424

c)

.0639

d)

.0196

8.

Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned?

a)

.0331

b)

.9619

c)

.9950

d)

.1488

9.

On a Sunday in April, dog bite victims arrive at Carver Memorial Hospital at a historical rate of 0.6 victim per day. On a given Sunday in April, what is the probability that exactly two dog bite victims will arrive?

a)

.0988

b)

.0919

c)

.0902

d)

.0875

10.

If tubing averages 16 defects per 100 meters, what is the probability of finding exactly 2 defects in a randomly chosen 10-meter piece of tubing?

a)

.3422

b)

.2674

c)

.8795

d)

.2584

11.

Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

a)

Poisson

b)

Binomial

c)

Hypergeometric

d)

None of the ones covered in class

12.

Which distribution is most nearly appropriate to describe .the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube?

a)

Poisson

b)

Binomial

c)

Hypergeometric

d)

None of the ones covered in class

13.

Which distribution is most nearly appropriate to describe .the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers

a)

Poisson

b)

Binomial

c)

Hypergeometric

d)

None of the ones covered in class

14.

Which distribution is most nearly appropriate to describe the number of births in a hospital until the first twins are delivered?

a)

Poisson

b)

Binomial

c)

Hypergeometric

d)

None of the ones covered in class

15.

A discrete random variable has a countable number of distinct values.

a)

True

b)

False

16.

The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

a)

True

b)

False

17.

A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.

a)

True

b)

False

18.

The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.

a)

True

b)

False

19.

Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

a)

True

b)

False

20.

The hypergeometric distribution is not applicable if sampling is done with replacement.

a)

True

b)

False

21.

The gender of a randomly chosen unborn child is a Bernoulli event.

a)

True

b)

False

22.

A discrete probability distribution:

a)

is a listing of all possible values of the random variable

b)

assigns a probability to each possible value of the random variable.

c)

can assume values between -1 and +1

d)

none of the above

23.

A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If it rolls to a 4, 5, or 6 you lose $1. Find the expected winnings.

a)

$0.50

b)

$3.00

c)

$1.50

d)

$1.00

24.

From recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed

machine are defective. What is the probability that out of six keyboards selected at random, exactly zero

keyboards will be defective?

a)

0.001

b)

0.167

c)

0.735

d)

0.500

25.

The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30

a.m.) for service are:

Number Probability

1 0.05

2 0.30

3 0.40

4 0.25

On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening?

a)

10.00

b)

1.00

c)

2.85

d)

1.96

26.

On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding

that none of them are absent?

a)

0.002

b)

0.344

c)

0.599

d)

0.100

27.

An insurance agent has appointments with four pr ospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

a)

0.250

b)

0.500

c)

0.410

d)

0.026

28.

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

a)

0.114

b)

0.887

c)

0.400

d)

0.231

29.

Chances are 50-50 that a newborn baby will be a girl. For families with five children, what is the probability that all the children are girls?

a)

0.900

b)

0.031

c)

0.001

d)

0.250

30.

A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes?

a)

0.001

b)

0.168

c)

0.667

d)

0.231

31.

A true-false test consists of six questions. If you guess the answer to each question, what is the probability of getting all six questions correct?

a)

0

b)

0.016

c)

0.062

d)

0.250

32.

What must you know to develop a binomial probability distribution?

a)

Probability of success

b)

Number of trials

c)

Number of successes

d)

"a" and "b" only

e)

"a" and "c" only

33.

In a Poisson distribution the mean is equal to

a)

nπ

b)

Σx n

c)

e - x

d)

$\frac{\mu^xe^{-\mu}}{x!}$

e)

zero

34.

In a Poisson distribution the variance is equal to

a)

nπ

b)

Σx n

c)

e - x

d)

$\frac{\mu^xe^{-\mu}}{x!}$

e)

zero

35.

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twentyfive customers buy gasoline at this station. What is the probability that at least ten pay in cash?

a)

0.416

b)

0.575

c)

0.586

d)

0.425

36.

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twentyfive customers buy gasoline at this station. What is the probability that no more than twenty pay in cash?

a)

0.0

b)

0.1

c)

0.9

d)

1.0

37.

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twentyfive customers buy gasoline at this station. What is the probability that more than ten and less than fifteen customers pay in cash?

a)

0.5410

b)

0.401

c)

0.380

d)

0.562

38.

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have no messages?

a)

0.0067

b)

zero

c)

0.0335

d)

Impossible to have no messages

39.

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages?

a)

0.0067

b)

0.875

c)

0.175

d)

1.0

40.

A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have two messages?

a)

0.0067

b)

0.0014

c)

0.420

d)

0.084

41.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the mean number of days absent?

a)

1.00

b)

0.40

c)

0.72

d)

2.5

42.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the variance of the number of days absent?

a)

1.99

b)

1.41

c)

5.00

d)

55.52

43.

If π = 1/3 and n = 900, what is the mean of this binomial distribution?

a)

100

b)

200

c)

300

d)

400

44.

If π = 1/5 and n = 100, what is the standard deviation of this binomial distribution?

a)

46

b)

5

c)

4

d)

1

45.

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?

a)

0.1353

b)

0.987

c)

0.576

d)

0.2134

46.

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of four every five minutes, what is the probability that more than four customers arrive in a five minute period?

a)

0.3711

b)

0.1231

c)

0.5412

d)

0.1111

47.

A numerical description of the outcome of an experiment is called a

a)

descriptive statistic

b)

probability function

c)

variance

d)

random variable

48.

A random variable that can assume only a finite number of values is referred to as a(n)

a)

infinite sequence

b)

finite sequence

c)

discrete random variable

d)

discrete probability function

49.

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

a)

uniform probability distribution

b)

binomial probability distribution

c)

hypergeometric probability distribution

d)

normal probability distribution

50.

Variance is

a)

a measure of the average, or central value of a random variable

b)

the square root of the standard deviation

c)

a measure of the dispersion of a random variable

d)

the sum of the squared deviation of data elements from the mean

51.

A continuous random variable may assume

a)

any value in an interval or collection of intervals

b)

only integer values in an interval or collection of intervals

c)

only fractional values in an interval or collection of intervals

d)

only the positive integer values in an interval

52.

A description of the distribution of the values of a random variable and their associated probabilities is called a

a)

probability distribution

b)

random variance

c)

random variable

d)

expected value

53.

Which of the following is a required condition for a discrete probability function?

a)

Σf(x) = 0

b)

f(x) ≥ 1 for all values of x

c)

f(x) < 0

d)

Σf(x) = 1

54.

A measure of the average value of a random variable is called a(n)

a)

variance

b)

standard deviation

c)

expected value

d)

coefficient of variation

55.

Which of the following is not a required condition for a discrete probability function?

a)

f(x) ≥ 0 for all values of x

b)

Σf(x) = 1

c)

Σf(x) = 0

d)

Σ(fx) ≥ 1

56.

The standard deviation is the

a)

variance squared

b)

square root of the sum of the deviations from the mean

c)

same as the expected value

d)

positive square root of the variance

57.

The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the

a)

square root of the deviations from the mean

b)

square root of the deviations from the median

c)

squared deviations from the median

d)

squared deviations from the mean

SB - Chapter 6

Total questions: 57

Worksheet time: 3hrs 51mins

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