75 70

II Trucks

ill Cars

65 60 55 0

........ - _ .. ---·--------------- - ---------·-··-·-- ] zs T

I

c. Draw a bar graph showing the results you derived in part (b). (5 points)

Cars Trucks Totals 55 .02 .07 .09 60 0 .03 .03 65 .22 .20 .42 70 .16 .1 1 .27 75 .10 .09 ..19

Totals I

.50 .50 1.00

b. Express the table you derived in part (a) in percentages based on the grand total. (5 points)

Cars Trucks Totals 55 2 7 9 60 0 3 3 65 22 20 42 70

I

16 11 27 75 10 9 19

Totals 50 50 100

a. Express the results in a contingency table using frequencies and showing all marginal totals. (5 points)

1. The National Highway System Designation Act of 199'5 allows states to set their own highway speed limits. Attached to the exam is the data for the maximum speed limits for cars and trucks (in miles per hour) in November 2008.

Name ------------ Exam#2 Show your work!!

~ MATH3070

SS(xy) = ------=62=---------- :Lxy=_~1o_s_5 _

SS(x) = 122

:L/ = -~13_32~----

b. Complete each of the following (1 point each):

Commercials, x 6 0 18 16 14 12 10 8 4 2

2 +----- ----------------~-·-------~·~-~----

4 ;----------------------- • •Sales Units, y •

-:-:-~~!--~-------~-~---_--_--_-----~~-=-~--~-=-- ---~-~~~~~~-~~~~~~~~.~~--=-_ -~~----_--=---~----.-- _-_------- --------1 1: ~'-------·-----~-------·---- !

a. Draw a scatter diagram of this data. (5 points)

City A B c D E F G H I J Commercials, x 12 6 9 15 11 15 8 16 12 6 Sales Units, y 7 5 10 14 12 9 6 11 11 8

2. A marketing firm wished to determine whether the number of television commercials broadcast was linearly correlated with the sales of its product. The data, obtained from several cities, are shown below:

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The slope tells us that for every additional commercial there is an increase of approximately Yi sales unit. The intercept tells us that without any commercials (x = 0) there are approximately 3. 7 sales units.

g. Interpret the meaning of the equation you found in part (f). (4 points)

b = SS(xy) = 72.1=0.508197 1 SS(x) 122

LY-b1LX 93-(0.508197)110 .37.09836 098.36 b - - - -3 7 0 - n - 10 - 10 - .

f. Using the numbers you provided in part (b) determine the regression line for this data, y = b0 + b,x . (4 points)

r2 = 0.437007 So, approximately 48% of the variation in the number of sa1es units is explained by the variation in the number of commercials shown.

e. What does the value of r2 tell you for this data? Explain. ( 4 points)

There is a fairly strong positive correlation between the number of commercials and the number of sales units.

d. What does this value of correlation seem to be telling you? Explain. (4 points)

62 = 0.661065 ..)122°72.l

SS(xy) r = ----;====="====

Jsscx)SS(y)

c. Using the numbers you provided in part (b) calculate the correlation coefficient r. (4 points)

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60%

b. If one chocolate is selected at random, what is the probability that it is milk chocolate? (5 points)

#nut+ #milk-choc - #both= 71-+44+60-#both = 71 -+#both =104-71 =33

All but 40 of them are milk chocolate .+60 Milk Chocolate, 40 Dark Chocolate all but 56 are nut -+ 56 Raisin, 44 Nut all but 29 are nut-filled or milk chocolate-+ 71 are nut or milk chocolate

Mille chocolate with nut filling ----'3'""""3'--- Milk chocolate with raisin filling --'"'2"--7 _

Dark chocolate with raisin filling -~2_3~· -~ Dark chocolate with nut filling~

a. How many of each type are there? ( 5 points)

4. A bowl contains 100 identical-looking, foil-wrapped, chocolate covered candies of four kinds. The candies are either milk or dark chocolate with either a nut or a raisin filling .. All but 40 of them are milk chocolate, all but 56 are nut, and all but 29 are nut-filled or milk chocolate.

3. A box contains one each of $1, $5, $10, $20 bills. Two bills are selected at random (without replacement); list the sample space as a tree diagram. (5 points)

Start

Page4

Two events are independent if the outcome of one has no impact on the outcome of the other.

b. Independent events

Mutually exclusive events cannot happen simultaneously.

a. Mutually exclusive events.

5. Define in your own words what each of the following means. (5 points each)

P(DCIR) = P(DC and R)/P(R) = .23/.56 = .4107

e. If one chocolate is selected at random, what is the probability that it is dark chocolate given it is raisin? (5 points)

P(DC and R) = .23

d. If one chocolate is selected at random, what is the probability that it is dark chocolate and raisin? (5 points)

P(DC or R) = P(DC) + P(R) - P(DC and R) = .4 + .56 - .23 = .73

c. If one chocolate is selected at random, what is the probability that it is dark chocolate or raisin? (5 points)

Page 5

P(Ra or Hermes) = P(Ra) + P(Hermes)- P(Ra and Hermes) = .40 + .32 - .09 =.61

Note: The answer is not 48% (the value given in the problem) since that excludes the people that knew Hermes or Ra but not Loki.

c. What is the probability that a person chosen at random from this group knew either Ra or Hermes were? (5 points)

12%

b. What is the probability that a person chosen at random from this group knew only who Loki was? (5 points)

http://mpeg.math.tamu.edu/Joe Kahlig/venn/mythology.html

25

Loki

a. Draw a Venn diagram illustrating this information. ( 5 points)

• 25 people did not know any of these. • 3 people knew all three. • 48 people knew who Hermes or Ra were but did not know who Loki was. • 40 people knew who Ra was. • 21 people knew who at least two of these were. • 7 people knew who Loki and Ra were but did not know who Hennes was. • 8 people knew who Loki and Hermes were.

6. I 00 people were asked if they knew who any of the following are: Loki, Hermes, and Ra.

Page6

r ques 10n State Cars Trucks State Cars Trucks Alabama 70 70 Montana 65 65 Alaska 65 65 Nebraska 75 75 Arizona 75 75 Nevada 75 75 Ark.ans as 70 65 New Hampshire 65 65 California 70 55 New Jersey 65 65 Colorado 75 75 New Mexico 75 75 Connecticut 55 55 New York 65 65 Delaware 65 65 North Carolina 70 70 Florida 70 70 North Dakota 70 70 Georgia 70 70 Ohio 65 55 Hawaii 55 55 Oklahoma 75 75 Idaho 75 75 Oregon 65 55 Illinois 65 55 Pennsylvania 65 65 Indiana 65 60 Rhode Island 65 65 Iowa 65 65 South Carolina 65 65 Kansas 70 70 South Dakota 75 65 Kentucky 65 65 Tennessee 65 65 Louisiana 70 70 Texas 70 60 Maine 65 65 Utah 75 75 Massachusetts 65 65 Vermont 65 65 Maryland 65 65 Virginia 65 65 Michigan 70 55 Washington 70 60 Minnesota 70 70 West Virginia 70 70 Mississippi 70 70 Wisconsin 65 65 Missouri 70 70 Wvoming 75 75

1 t Data fo