1. A variable y of a finite population has the frequency distribution shown in the table. Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained. Complete parts(a) through(d) below.

Y F

4 1

5 1

6 5

7 3

a. Determine the probability distribution of the random variable Y.

Y- 4. 5 6 7

P( Y=y) ( ? ) ( ? ) ( ? ) ( ? )

(Type integers or decimals. Do notround.)

b. Userandom-variable notation to describe the events that Y takes on the value 3, a value less than 3, and a value of at least 3.

c. Find P(Y=3), P(Y<3), and P(Y3).

d. Construct a probability histogram for the random variable Y.

2 A certain hurricane database extends back to1851, recording among other data the number of major hurricanes(measuring at least a Category3) striking a certain region per year. The following table provides a probability distribution for the number of majorhurricanes, Y, for a randomly selected year between 1851 and 2012. Complete parts(a) through(f) below.

a. Userandom-variable notation to represent the event that the year had at least one major hurricane. Select the correct choice below and fill in the answer box within your choice.

A. ( ? )

B.( ? )

b. Userandom-variable notation to represent the event that the year had exactly six major hurricanes.

c. Userandom-variable notation to represent the event that the year had between 5 and 7 majorhurricanes, inclusive.

d. Use the special addition rule and the probability distribution to determine the probability that the year had at least one major hurricane.

e. Use the special addition rule and the probability distribution to determine the probability that the year had exactly six major hurricanes.

f. Use the special addition rule and the probability distribution to determine the probability that the year had between 5 and 7 majorhurricanes, inclusive.

3 In a certainstate, through the observation of female black bears and theirlitters, the following estimate is given for the probability distribution of the number of young per litter for female black bears in the state. Complete parts(a) and(b) below.

Litter size Probability

1 0.191

2 0.618

3 0.137

4 0.054

a. Explain why the probabilities in the table provide only an estimate of the true probabilities. Choose the correct answer below.

A.The probabilities are only an estimate of the true probabilities because the data were obtained from the complete population of black bears including both males and females in the state.

B.The probabilities are only an estimate of the true probabilities because the data were calculated theoretically based on previous observations of female black bears from the state.

C.The probabilities are only an estimate of the true probabilities because the data were obtained from the complete population of female black bears in the state.

D.The probabilities are only an estimate of the true probabilities because the data were gathered from a sample of female black bears from the state.

b. Estimate the probability that a black bear in this state has a litter of either twoorfour cubs.

4 Suppose T and Z are random variables.

a. If P(T>2.01)=0.03 and P(T<2.01)=0.03, obtain P(2.01T2.01).

b. If P(1.29Z1.29)=0.80 and also P(Z>1.29)=P(Z<1.29). Find P(Z>1.29).

a. P(2.01T2.01)= ( ? )

5 The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.

x P(X=x)

2 0.026

4. 0.048

5 0.344

6 0.220

7 0.356

8. 0.006

a. Find and interpret the mean of the random variable.

Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice.

(Round to three decimal places asneeded.)

A.The average number of persons in a shuttle crew is ( ? ) person(s).

B.The most common number of persons in a shuttle crew is ( ? ) person(s).

b. Obtain the standard deviation of the random variable.

c. Construct a probability histogram for the randomvariable; locate themean; and showone-, two-, andthree-standard-deviation intervals

6 The accompanying table provides a probability distribution for the number of majorhurricanes, Y, for a randomly selected year between 1851 and 2012. Complete parts(a) through(c) below.

y P(Y=y)

0 0.186

1 0.259

2 0.215

3 0.093

4 0.045

5 0.056

6. 0.022

7 0.012

8 0.112

a. Find and interpret the mean of the random variable.

b. Obtain the standard deviation of the random variable.

c. Draw a probability histogram for the random variable.

7 The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is given below.

y P(Y=y)

2 0.027778

3 0.055556

4. 0.083333

5 0.111111

6 0.138889

7 0.166667

8 0.138889

9 0.111111

10 0.083333

11 0.055556

12 0.027778

b. Obtain the standard deviation of the random variable

8 A game of chance is played on a wheel that contains 34 numbers (16 arered, 16 areblack, and 2 aregreen). When the wheel isspun, the ball is equally likely to land on any of the 34 numbers. Suppose that you bet $9 on black. If the ball lands on a black number, you win $9; otherwise you lose your $9. Let X be the amount you win on your $9 bet. Then X is the random variable whose probability distribution is as follows.

X P ( X=x )

9 0.471

-9 0.529

a. Find the expected value of the random variable X

b. Onaverage, how much will you lose perplay?

c. Approximately how much would you expect to lose if you bet $9 on black 100 times? 1000 times?

d. Is the game profitable toplay? Explain.

9 A factory manager collected data on the number of equipment breakdowns per day. From thosedata, she derived the probability distribution shown to theright, where W denotes the number of breakdowns on a given day. Answer parts a through c.

w P (W=w)

0 0.65

1 0.20

2 0.15

a. Determine W and W. (Type an integer or adecimal.)

b. Onaverage, how many breakdowns occur perday?

c. About how many breakdowns are expected during a1-year period, assuming 250 work days peryear?

13 The probability is 0.4 that a traffic fatality involves an intoxicated oralcohol-impaired driver or nonoccupant. In ten trafficfatalities, find the probability that thenumber, Y, which involve an intoxicated oralcohol-impaired driver or nonoccupant is...

a. exactlythree; at leastthree; at most three.

b. between two and four, inclusive.

c. Find and interpret the mean of the random variable Y.

d. Obtain the standard deviation of Y.

a. The probability that exactly three traffic fatalities involve an intoxicated oralcohol-impaired driver or nonoccupant is ( ?) (Round to four decimal places asneeded.)

14 According to anarticle, 39% of adults have experienced a breakup at least once during the last 10 years. Of nine randomly selectedadults, find the probability that thenumber, X, who have experienced a breakup at least once during the last 10 years is

a. exactlyfive; at mostfive; at least five.

b. at leastone; at most one.

c. between three and five, inclusive.

d .Determine the probability distribution of the random variable X.

e. Strictlyspeaking, why is the probability distribution that you obtained in part(d) only approximatelycorrect? What is the exact distributioncalled?

a. The probability that exactly five adults have experienced a breakup at least once during the last 10 years is ( ? )

(Round to three decimal places asneeded.)