devry math399n week 5 quiz latest 2016 july

devry math399n week 5 quiz latest 2016 july

1.Decide whether the random variable x is discrete or continuous.

x represents

the annual vehicle ?miles driven in the United States.

Is the random variable x discrete or continuous? Choose the correct answer below.

Discrete

Continuous

2. A standard deck of cards contains 52 cards. One card is selected from the deck.

(a)

Compute the probability of randomly selecting

a

king

or

three.

(b)

Compute the probability of randomly selecting

a

king

or

three

or

seven

(c)

Compute the probability of randomly selecting

aa

jackj

or

spade

a.

P(king

or

three)=

(Type an integer or a simplified fraction.)

b.

P(king

or

three

or

seven)equals=

(Type an integer or a simplified fraction.)

c.

P(jack

or

spade)equals=

(Type an integer or a simplified fraction.)

3.

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

n equals n=128,

p =0.56

The mean,

?,

is

(Round to the nearest tenth as needed.)

The variance,

?2,

is

(Round to the nearest tenth as needed.)

The standard deviation,

?,

is

(Round to the nearest tenth as needed.)

4.

Use technology to (a) construct and graph a probability distribution and (b) describe its shape.

The number of computers per household in a small town

Computers 0 1 2 3

Households 296 280 97 18

(a) Construct the probability distribution by completing the table below.

x P(x)

0

1

2

3

(Round to three decimal places asneeded.)

Choose the correct graph of the probability distribution.

A.

01230.10.20.30.40.5Number of ComputersP(x)x

x y graph

.

B.

01230.10.20.30.40.5Number of ComputersP(x)x

x y graph

C.

01230.10.20.30.40.5Number of ComputersP(x)x

The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution. 0123450.000.100.200.300.40xP(x)0.050.250.330.140.150.08

x y graph

The mean is

(Round to two decimal places as needed.)

The variance is

(Round to four decimal places as needed.)

The standard deviation is

(Round to four decimal places as needed.)

The expected value is

.

(Round to two decimal places as needed.)

6.

Researchers found that people with depression are

fourfour

times more likely to have a breathing-related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?

Identify the two events. Choose the correct answer below.

A.

Having a breathing-related sleep disorder and not having it

B.

Depression and breathing-related sleep disorder

C.

Research and depression

D.

Research and breathing-related sleep disorder

Are the events independent or depedent?

Independent

Dependent

7.

Use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.

not between 45 and 64 years oldbetween 45 and 64 years old

Ages of voters FrequencyFrequency

18 to 20 5.15.1

21 to 24 8.48.4

25 to 34 23.923.9

35 to 44 25.525.5

45 to 64 55.955.9

65 and over 27.727.7

The probability is

(Round to three decimal places as needed.)

8.

Given that x has a Poisson distribution with

?=1.2,

what is the probability that

xequals=0?

P(0)?

(Round to four decimal places as needed.)

9.

The table below shows the results of a survey in which

141

men and

146

women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. Complete parts (a) through (d).

Men Women Total

Less than one month's income 65 84 149

One month's income or more

76 62 138

Total 141 146 287

(a) Find the probability that a randomly selected worker has one month's income or more set aside for emergencies.

The probability is

(Round to the nearest thousandth as needed.)

(b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month's income.

The probability is

(Round to the nearest thousandth as needed.)

(c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is a female.

The probability is

(Round to the nearest thousandth as needed.)

(d) Are the events "having less than one month's income saved" and "being male" independent or dependent?

Dependent

.

Independent

10.

A survey asks

1400

workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?"

FFifty-five

percent of those surveyed say they are reducing the amount of vacation.

Twenty

workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

No

Yes

\.

What is a success in this experiment?

Selecting a worker who is not reducing the amount of vacation

Selecting a worker who is reducing the amount of vacation

This is not a binomial experiment.

Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice.

A.

n =

Your answer is correct.

B.

This is not a binomial experiment.

Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice.

A.

p =

(Type an integer or a decimal.)

Your answer is correct.

B.

This is not a binomial experiment.

Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.

A.

q =

(Type an integer or a decimal.)

Your answer is correct.

B.

This is not a binomial experiment.

List the possible values of the random variable x.

x =1,

2,..., 20

x =0,

1, 2,..., 20

.

x=1,

2, 3,..., 1400

This is not a binomial experiment.

Question is complete.

11.

During a 52-week period, a company paid overtime wages for

19

weeks and hired temporary help for

8

weeks. During

5

weeks, the company paid overtime and hired temporary help. Complete parts (a) and (b) below.

(a) Are the events "selecting a week that contained overtime wages" and "selecting a week that contained temporary help wages" mutually exclusive?

No

Yes

(b) If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages?

P(overtime wages or temporary help wages) =

(Round to the nearest thousandth as needed.)

12.

A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution on the right shows the results. Use the table to answer the following question.

What is the probability that the next person surveyed is very prepared?

Response FrequencyFrequency

Very prepared 261261

Somewhat prepared 980980

Not too prepared 595595

Not at all prepared 301301

Not sure 7474

The probability the next person surveyed is very prepared is

.

(Round to three decimal places as needed.)

13.

Determine the required value of the missing probability to make the distribution a discrete probability distribution. x P(x)

3 0.22

4 ?

5 0.38

6 0.21

P(4) =

??

(Type an integer or a decimal.)

14.

32%

of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two,

and (c) between two and five inclusive. If convenient, use technology to find the probabilities.

(a)

P(2)=

(Round to the nearest thousandth as needed.)

(b)

P(x>2)=

(Round to the nearest thousandth as needed.)

(c)

P(2?x?5)=

(Round to the nearest thousandth as needed.)

15.

A doctor gives a patient a

80%

chance of surviving bypass surgery after a heart attack. If the patient survives the surgery, then the patient has a

45%

chance that the heart damage will heal. Find the probability that the patient survives the surgery and the heart damage heals.

The probability is

(Type an integer or a decimal.)

16.

The table below shows the results of a survey that asked

1074

adults from a certain country if they would support a change in their country's flag. A person is selected at random. Complete parts (a) through (d).

Support?? Oppose Unsure Total

Males 172 324 15 511

Females 240 297 26 563

Total 412 621 41 1074

(a) Find the probability that the person opposed the change or is female.

P(opposed the change or female)=

(Round to the nearest thousandth as needed.)

(b) Find the probability that the person supports the change or is male.

P(supports the change or male

(Round to the nearest thousandth as needed.)

(c) Find the probability that the person is not unsure or is female.

p (not unsure or female)=

(Round to the nearest thousandth as needed.)

(d) Are the events "being male" and "support" mutually exclusive? Explain.

A.

Yes, because one can't be male and support the change at the same time.

B.

Yes, because there are

172

males that support the change.

C.

No, because there are

172

males that support the change.

D.

No, because one can't be male and support the change at the same time.