1. Students at a major university are complaining of a serious housing crunch. They complain that many students have to commute too far to school because there is not enough housing near campus. University officials respond with the following information: the mean distance commuted to school by students is14.2miles, and the standard deviation of the distance commuted is3.4miles

Assuming that the university officials' information is correct, complete the following statements about the distribution of commute distances for students at this university

a.) According to Chebyshev's theorem, at least [Choose one] (36%,56%,75%,84%,89%) of the commute distances lie between7.4miles and21.0miles.

b.) According to Chebyshev's theorem, at least84%of the commute distances lie between miles and miles.

(Round your answer to 1 decimal place.)

2.)A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was40years old, with a standard deviation of 11years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers

a.) According to Chebyshev's theorem, at least36%of the home buyers' ages lie between _ years and _ years. (Round your answer to the nearest whole number.)

b.) According to Chebyshev's theorem, at least [Choose one] (36%,56%,75%,84%,89%) of the home buyers' ages lie between18years and62years.

3.)A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of20 to80. In a recent year, the national mean score for the writing section was47.3, with a standard deviation of10.8. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.

a.) According to Chebyshev's theorem, at least [Choose one] (36%,56%,75%,84%,89%) of the scores lie between25.7and68.9.

b.) According to Chebyshev's theorem, at least56%of the scores lie between and. (Round your answer to 1 decimal place.)

4.) Fill in theP= (X=x)values to give a legitimate probability distribution for the discrete random variableX, whose possible values are2,3,4,5, and6.

ValuexofX	P= (X=x)
2	0.27
3	0.26
4	0.12
5
6

5.) Fill in theP= (X=x)values to give a legitimate probability distribution for the discrete random variableX, whose possible values are -2,1,2,5 and 6.

Value x of X	P = (X= x)
2
1	0.18
2	0.29
5
6	0.25

6.) Fill in theP= (X=x)values to give a legitimate probability distribution for the discrete random variableX, whose possible values are -3,2,1,5, and6

Value xof X	P =(X=x)
3	0.10
2	0.18
1	0.28
5
6

7. An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth,ttt, etc.

For each outcome, letNbe the random variable counting the number of tails in each outcome. For example, if the outcome istht, then=Ntht2. Suppose that the random variableXis defined in terms ofNas follows:=X4N2N2-3. The values ofXare given in the table below.

Outcome	thh	hhh	hth	tth	tht	ttt	htt	hht
Value of X	1	3	1	3	3	9	3	1

Calculate the probabilitiesP=(X=x)of the probability distribution ofX. First, fill in the first row with the values ofX. Then fill in the appropriate probabilities in the second row.

Value x of X
P = (X=x)

8.) An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we writehth,ttt, etc. For each outcome, letN be the random variable counting the number of heads in each outcome. For example, if the outcome istth, then=N (tth)1. Suppose that the random variableXis defined in terms ofNas follows:=XN2N-4. The values ofX are given in the table below.

Outcome	tht	hhh	thh	hth	ttt	tth	hht	htt
Value of X	-4	2	-2	-2	-4	-4	-2	-4

Calculate the probabilitiesP=(X=x)of the probability distribution ofX. First, fill in the first row with the values ofX. Then fill in the appropriate probabilities in the second row

Value x of X
P = (X=x)

9.) An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sortoee(meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll).

For each outcome, letNbe the random variable counting the number of odd rolls in each outcome. For example, if the outcome iseoe, then=N eoe

Suppose that the random variableXis defined in terms ofNas follows:

X= 2N-2. The values ofXare given in the table below.

Outcome	oeo	eeo	eoe	eee	ooe	eoo	ooo	oee
Value of X	2	0	0	2	2	2	4	0

Calculate the probabilitiesP=(X=x)of the probability distribution of

X. First, fill in the first row with the values ofX. Then fill in the appropriate probabilities in the second row.

Value x of X
P = (X=x)

10.) LetXbe a random variable with the following probability distribution.

Value x of X	P = (X=x)
30	0.15
40	0.20
50	0.30
60	0.35

Complete the following.

(a) Find the expectationE (X)ofX

E (X) = _

(b) Find the variance Var (X)ofX.

Var (X) = _

11.) LetXbe a random variable with the following probability distribution

Value x of X	P = X x
4	0.05
5	0.25
6	0.15
7	0.15
8	0.40

Complete the following.

(a) Find the expectationE XofX.

E (X) = _

(b) Find the variance VarXofX.

Var (X) = _

12.) LetXbe a random variable with the following probability distribution.

Value x of X	P =(X=x)
0	0.30
10	0.25
20	0.20
30	0.25

Complete the following

a.) Find the expectationEXofX.

E (X) =

b.) Find the variance VarXofX.

Var (X) =

13.) Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While talking to her on the phone, we'll thoroughly shuffle a standard deck of52 cards (which is made up of13hearts,13spades,13diamonds, and13clubs) and draw one card at random. We'll ask Clara to name the suit (heart, spade, diamond, or club) of the card we drew. After getting her guess, we'll return the card to the deck, thoroughly shuffle the deck, draw another card, and get her guess for the suit of this second card. We'll repeat this process until we've drawn a total of16 cards and gotten her suit guesses for each.

Assume that Clara is not clairvoyant, that is, assume that she randomly guesses on each card.

Answer the following

a.) Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response

_

b.) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

_

14.) Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go") so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that45% of its customers order their food to go. Suppose that this proportion is correct and that a random sample of40individual customers is taken.

Answer the following.

a.) Estimate the number of customers in the sample who order their food to go by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

_

b.) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

_

15.) Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of20Colonials games.

Answer the following.

a.) Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response

_

b.) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

_

16.) A TV executive is interested in the popularity of a particular streaming TV show. She has been told that a whopping65%of American households would be interested in tuning in to a new network version of the show. If this is correct, what is the probability that all6of the households in her city being monitored by the TV industry would tune in to the new show? Assume that the 6households constitute a random sample of American households.

Round your response to at least three decimal places

17.) The unemployment rate in a city is14%. If10people from the city are sampled at random, find the probability that fewer than2of them are unemployed. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

18.) From experience, an airline knows that only70%of the passengers booked for a certain flight actually show up. If6passengers are randomly selected, find the probability that more than4of them show up.

Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.

19.) Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If4Colonials games are chosen at random, what is the probability that exactly2of those games are won by the Colonials?

Round your response to at least three decimal places.

20.) A multiple-choice test consists of9questions. Each question has answer choices ofa,b,c, andd, and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets at most2of them correct?

Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.