1. 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 was43years old, with a standard deviation of10years. 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 least [Choose one] (36%,56%,75%,84%,89%) of the home buyers' ages lie between23years and63 years.

b.) 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.)

2.) Fill in theP= (X=x)values to give a legitimate probability distribution for the discrete random variableX, whose possible values are4,3,4,5, and6

Value x of X	P =(X=x)
4	0.13
3	0.12
4
5	0.12
6

3.) 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 is ttt, then=N (ttt)=0. Suppose that the random variableXis defined in terms ofN

as follows:X=2N2- 6N -2. The values ofXare given in the table below.

Outcome	hth	tht	hht	tth	htt	hhh	ttt	thh
Value of X	6	6	6	6	6	2	2	6

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)

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

Value x of X	P = (X=x)
3	0.45
4	0.10
5	0.15
6	0.30

Complete the following

a.) Find the expectationE(X)ofX

E (X) =

b.) Find the variance Var (X)ofX

Var (X) =

5.)A rainstorm in Portland, Oregon, wiped out the electricity in5%of the households in the city. Suppose that a random sample of60Portland households is taken after the rainstorm.

Answer the following

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

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

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6.) The workers' union at a particular university is quite strong. About

96%of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview4workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly2of the workers interviewed are union members?

Round your response to at least three decimal places

7.) A machine that manufactures automobile parts produces defective parts

14%of the time. If6parts produced by this machine are randomly selected, what is the probability that fewer than2of the parts are defective?

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

8.) 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 is17.7miles, and the standard deviation of the distance commuted is3.3 miles.

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 least8/9(about89%) of the commute distances lie between _ miles and _ miles.

(Round your answer to 1 decimal place.)

b.) According to Chebyshev's theorem, at least [Choose one] (36%,56%,75%,84%,89%) of the commute distances lie between11.1miles and24.3miles

9.)Fill in theP= (X=x)values to give a legitimate probability distribution for the discrete random variableX, whose possible values are0,2,3,4, and6.

Value x of X	P = (X=x)
0	0.15
2	0.16
3
4
6	0.27

10.) A machine that manufactures automobile pistons is estimated to produce a defective piston3%of the time. Suppose that this estimate is correct and that a random sample of80pistons produced by this machine is taken.

Answer the following.

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

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

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