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QNT 275 Week 3 Practice: Connect Knowledge Check

The mean of a standard normal distribution is always equal to 1.

True

False

According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the mean number of individuals having group A blood.

1.2

1.44

2.4

1.55

Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6 and the probability that you will get a grade of B or better in Introduction to Accounting is .5. If these events are independent, what is the probability that you will receive a grade of B or better in both courses?

0.600

0.300

0.833

0.800

0.500

Probabilities must be assigned to sample space outcomes so that the probability assigned to each sample space outcome must be between ____________, inclusive.

0 and 1

-100 and 100

0 and 100

-1 and 1

Find z when the area between 0 and z is .4750.

0.68

1.96

−0.68

−1.96

The _____________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out.

outcome

probability

intersection

observation

The method of assigning probabilities when all outcomes are equally likely to occur is called the classical method.

True

False

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

True

False

In a statistical study, the random variable X = 1 if the house is colonial, and X = 0 if the house is not colonial. The random variable X is continuous.

True

False

If A and B are independent events, P(A) = .2, and P(B) = .7, determine

0.50

0.76

0.14

0.24

0.90

Given that X is a normal random variable, the probability that a given value of X is below its mean is ________________.

1

less than 0.5

equal to 0.5

greater than 0.5

The standard deviation of a standard normal distribution is always equal to 1.

True

False

If events A and B are mutually exclusive, then P(A∩B) is always equal to zero.

True

False

The normal probability distribution is a discrete probability distribution.

True

False

A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ____________ distribution.

exponential

uniform

binomial

normal

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received in a week exceed 200?

50%

0%

25%

100%

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.

Are D and C mutually exclusive?

Yes, mutually exclusive.

No, not mutually exclusive.

The mean of a standard normal distribution is always equal to ____________.

1

−1

0

0.5

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the standard deviation of the temperature increase?

4.33

7.50

10.12

1.25

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the standard deviation of the temperature increase?

4.33

7.50

10.12

1.25

Determine whether these two events are mutually exclusive: consumer with an unlisted phone number and a consumer who does not drive.

mutually exclusive

not mutually exclusive

Which of the following is not a discrete random variable?

the number of times a light changes red in a 10-minute cycle

the number of criminals found in a five-mile radius of a neighborhood

the number of minutes required to run 1 mile

the number of defects in a sample selected from a population of 100 products

If the random variable x is normally distributed, 68.26 percent of all possible observed values of x will be within two standard deviations of the mean.

True

False

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru third?

5/6

6/6

1/6

1/2

1/3

It is very common for television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected.

What is the probability that all three households viewed this special show?

0.127

0.726

0.382

0.146

0.056

In a binomial experiment, the results of one trial are dependent on the results of other trials.

True

False

In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is male and has a favorable opinion.

0.62

0.25

0.55

0.40

0.65

Probabilities must be assigned to each sample space outcome so that the probabilities of all the sample space outcomes add up to _____________.

between 0 and 1

between -1 and 1

0

1

If the random variable of x is normally distributed, _____ percent of all possible observed values of x will be within two standard deviations of the mean.

95.00

68.26

99.73

95.44

If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean.

None of the other choices is correct.

68.26

99.73

95.44

100

Which of the following statements about the binomial distribution is not correct?

Trials are independent of each other.

Each trial results in a success or failure.

The experiment consists of n identical trials.

The probability of success remains constant from trial to trial.

The random variable of interest is continuous.

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.

Are R and C mutually exclusive?

No, not mutually exclusive.

Yes, mutually exclusive.

A random variable is a numerical value that is determined by the outcome of an experiment.

True

False

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will fewer than 160 boxes of supplies arrive in a week?

2.28%

4.56%

42.07%

57.93%

The z value tells us the number of standard deviations that a value x is from the mean.

True

False

An event is a collection of sample space outcomes.

True

False

Determine whether these two events are mutually exclusive: consumer with an unlisted phone number and a consumer who does not drive.

not mutually exclusive

mutually exclusive

Determine whether these two events are mutually exclusive: unmarried person and a person with an employed spouse.

not mutually exclusive

mutually exclusive

Which of the following statements about the binomial distribution is not correct?

Each trial results in a success or failure.

Trials are independent of each other.

The experiment consists of n identical trials.

The random variable of interest is continuous.

The probability of success remains constant from trial to trial.

For a continuous random variable x, the height of the probability curve f(x) at a particular point indicates the value of the probability for that value.

True

False

An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that all five will be repaired on the same day?

.2373

.9990

.0010

.6328

A standard normal distribution has a mean of ____________ and standard deviation of ____________.

zero, one

zero, zero

one, zero

one, one

A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel?

5/26

21/26

1/26

4/26

The set of all possible outcomes for an experiment is called a(n) ____________.

event

probability

sample space

experiment

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

5/15

2/15

1/15

3/15