1.	A die is rolled and a coin is flipped simultaneously.  The number rolled on the die and whether the coin lands heads or tails is recorded.  How many outcomes are in the sample space?	
	A)  8    B)  6    C)  10    D)  12	

2.	Two coins are flipped at the same time and it is recorded whether each coin lands heads or tails.  The sample space for this is	
	A)  {H, T}.    B)  {HH, HT, TT}.    C)  {HH, HT, TH, TT}.    D)  {H, H, T, T}.	

3.	A spinner numbered 1 through 10 is spun and one die is tossed simultaneously.  The number spun and the number rolled are recorded.  How many outcomes are in the sample space?	
	A)  60    B)  16    C)  10    D)  6	

4.	A spinner numbered 1 through 10 is spun and one die is rolled simultaneously.  The sum of the number spun and the number rolled is recorded.  How many outcomes are in the sample space?	
	A)  60    B)  16    C)  15    D)  10	

5.	Three dice are tossed.  The number rolled on each die is recorded.  How many outcomes are in the sample space?	
	A)  18    B)  72    C)  216    D)  42	

6.	Three dice are tossed.  The sum of the numbers rolled is recorded.  How many outcomes are in the sample space?	
	A)  18    B)  12    C)  16    D)  72	

7.	Three dice are rolled and the number rolled on each die is recorded.  The outcomes in the sample space are all equally likely.	
	A)  True    B)  False	

8.	Three dice are rolled and the sum of the numbers rolled is recorded.  The outcomes in the sample space are all equally likely.	
	A)  True    B)  False	

9.	Two coins are flipped and the number that landed on heads is recorded.  The outcomes in the sample space are all equally likely.	
	A)  True    B)  False	

10.	Two coins are flipped and whether each one landed heads or tails is recorded.  The outcomes  in the sample space are all equally likely.	
	A)  True    B)  False	

11.	There are seven blue and six black socks in a drawer. One is pulled out at random. Find the probability that it is black.	
	A)  6/13    B)  6/7    C)  1/2    D)  1/6	

12.	Two fair dice are rolled and the sum rolled is recorded.  Find the probability that the sum is 4.	
	A)  1/3    B)  1/12    C)  4/11    D)  1/9	

13.	A fair coin is tossed three times.  Find the probability of getting exactly two heads.	
	A)  1/2    B)  1/3    C)  2/3    D)  3/8	

14.	If a fair die is rolled once, what is the probability of getting a number less than five?	
	A)  1/6    B)  1/2    C)  2/3    D)  5/6	

15.	A computer is programmed to randomly print two letters in a row without repeating a letter.  What is the probability that the first combination printed is the word "DO"?	
	A)  1/650    B)  1/325    C)  2/325    D)  1/26	

16.	We need to create three-digit code numbers that must begin with a 7. How many such codes can be made?	
	A)  700    B)  107    C)  100    D)  27	

17.	We need to create serial numbers that start with one of the letters a, b, c, d, or f, followed by three non-repeating digits.  How many serial numbers can be created?	
	A)  5000    B)  2520    C)  725    D)  3600	

18.	We need to create code words that use three letters of the alphabet.  Repeating of letters is allowed.  How many code words can be created?	
	A)  17,576    B)  15,600    C)  78    D)  75	

19.	A computer system requires users to have an access code that consists of a three-digit number that is not allowed to start with zero and cannot repeat digits.  How many such codes are possible?	
	A)  990    B)  648    C)  729    D)  720	

20.	The Olympic flag consists of five intertwined circles, one in each of the colors black, blue, green, red, and yellow.  What is the probability that a random coloring of the five circles using these colors will produce the exact match of the Olympic symbol?	
	A)  1/5    B)  1/3125    C)  5/120    D)  1/120	

21.	Either Terry, Chris, or Kim will attend a party.  The probability Terry attends is 0.31 and the probability Chris attends is 0.5.  What is the probability that Kim attends?	
	A)  0.33    B)  0.5    C)  0.81    D)  0.19	

22.	If there is a 0.8 probability of rain today, what is the probability it will not rain?	
	A)  0.8    B)  0.5    C)  0.2    D)  0.1	

23.	A sample space has three outcomes, A, B, and C.  The probability of outcome A is 0.39 and the probability of outcome B is 0.25.  What is the probability of outcome C?	
	A)  0.36    B)  0.33    C)  0.5    D)  0.64	

24.	A sample space contains three outcomes, A, B, and C.  Which of the following could be a legitimate assignment of probabilities to the outcomes? 

25.	A sample space consists of three outcomes, X, Y, and Z.  Which of the following could be a legitimate assignment of probabilities to the outcomes? 

26.	A raffle ticket costs $5.  First and second prize winners will be drawn at random.  The probability of winning the $100 first prize is 1/40 and the probability of winning the $25 second prize is 1/20.  What is the mean winnings for one play, taking into account the $5 cost of the ticket?	
	A)  –1.25    B)  –0.875    C)  3.375    D)  3.75	

27.	Suppose a game has three outcomes, A, B, and C with probabilities P(A) = 0.2, P(B) = 0.3, and P(C) = 0 .5.  A player will receive $3 when outcome A occurs, $4 when outcome B occurs, and will have to pay $2 when outcome C occurs.  What is the mean value of one trial of the game?	
	A)  0.80    B)  1.66    C)  1.00    D)  5.00	

28.	At a certain discount store, the number of people in checkout lines varies.  The probability model for the number of people in a randomly chosen line is

Number in line	
0	
1	
2	
3	
4	
5	

Probability	

0.08	

0.15	

0.20	

0.22	

0.15	

0.20	

What is the mean number of people in a line?	
	A)  2.5    B)  15.92    C)  2.81    D)  2.89	

29.	A fair die is rolled.  If a number 1 or 2 appears, you will receive $5.  If any other number appears, you will pay $2.  What is the mean value of one trial of this game?	
	A)  $1/3    B)  $3    C)  $3/2    D)  –$3	

30.	The marketing department of an electronics manufacturer has done research on the number of television sets owned by families in a large town.  The probability model for the number of sets owned by a randomly chosen family is given below.  What is the mean number of sets per family?

Number of sets	
0	
1	
2	
3	

Probability	

0.04	

0.34	

0.47	

0.15	

	A)  0.96    B)  1.5    C)  1.77    D)  1.73	

31.	The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years.  What is the upper quartile of battery shelf life?	
	A)  4.0025 years    B)  4.25 years    C)  4.17 years    D)  5.25 years	

32.	The length of students' college careers at Anytown University is known to be normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years.  What is the lower quartile for the length of students' careers at Anytown University?	
	A)  4.83 years    B)  3.75 years    C)  4.3275 years    D)  2.75 years	

33.	The scores of students on standardized test form a normal distribution with a mean of 300 and a standard deviation of 40.  What are the lower- and upper-quartile scores for this test?	
	A)  299.33 and 300.67    B)  273.2 and 326.8    C)  260 and 340    D)  150 and 450	

34.	The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours.  Assuming the distribution of study times is normal, what percent of students spend more than 25.238 hours per week on homework?	
	A)  16.5%    B)  5%    C)  12.5%    D)  25%	

35.	The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40.  What is the probability that a randomly chosen student scores below 273.2 on the test?	
	A)  0.025    B)  0.25    C)  0.165    D)  0.125	

36.	The annual income of residents in a county is $42,000 with a standard deviation of $10,000.  Between what two values do 95% of the incomes of county residents lie?	
A)	$40,000 and $44,000	C)	$32,000 and $52,000	
B)	$22,000 and $62,000	D)	$30,000 and $50,000	

37.	The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years.  What range of years contains 68% of all battery shelf lives?	
	A)  2 to 5 years    B)  2.5 to 4.5 years    C)  2.83 to 4.17 years    D)  2.75 to 4.25	

38.	The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40.  Between what two values do 99.7% of the test scores lie?	
	A)  260 to 340    B)  220 to 380    C)  297 to 303    D)  180 to 420	

39.	The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours.  Assuming the distribution of study times is normal, what percent of students study between 22.9 and 25.7 hours?	
	A)  99.7%    B)  95%    C)  68%    D)  50%	

40.	The length of students' college careers at Anytown University is known to be normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years.  What percent of students have college careers lasting between 2 and 9 years?	
	A)  50%    B)  99.75    C)  68%    D)  95%	

41.	The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years.  What percent of batteries last between 1.25 and 5.75 years?	
	A)  99.7%    B)  95%    C)  68%    D)  50%	

42.	The annual income of residents in a certain county is normally distributed, with a mean of $42,000 and a standard deviation of $10,000.  What is the probability that a randomly chosen resident has income over $52,000?	
	A)  16%    B)  32%    C)  50%    D)  68%	

43.	The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces.  What is the probability that a randomly chosen bag will weigh less than 14.6 ounces?	
	A)  50%    B)  5%    C)  2.5%    D)  2%	

44.	The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces.  What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?	
	A)  5%    B)  2.5%    C)  0.3%    D)  0.15%	

45.	Using the Central Limit Theorem for a normally distributed variable, how would the standard deviation of the sample mean for a sample of size 200 be related to that of size 3200?	
A)	It would be one-sixteenth as large.	C)	It would be four times as large.	
B)	It would be one-fourth as large.	D)	It would be sixteen times as large.	

46.	The weight of bags of potato chips produced by one machine at a packaging plant has a standard deviation of 0.2 oz.  Suppose a sample of 25 bags is drawn from a production run and weighed.  What is the standard deviation sx of the mean result?	
	A)  0.008    B)  0.04    C)  0.2    D)  1.0	

47.	A poll of 60 students found that 20% were in favor of raising parking fees to pave two new parking lots.  The standard deviation of this poll is about 5.2%.  What would be the standard deviation if the sample size was increased from 60 students to 120 students?	
	A)  10.4%    B)  7.3%    C)  2.6%    D)  3.68%	

48.	The batteries used by a calculator have useful lives that follow a normal distribution, with an average life of 2000 hours and a standard deviation of 200 hours.  In the production process, the manufacturer draws random samples of 100 batteries and determines the mean useful life of the sample.  What is the standard deviation sx of this mean?	
	A)  25 hours    B)  100 hours    C)  2 hours    D)  20 hours	

49.	A poll of 60 students found that 20% were in favor of raising parking fees to pave two new parking lots.  The standard deviation of this poll is about 5.2%.  How large a sample would be needed to reduce this standard deviation to 2.6%?	
	A)  30    B)  1200    C)  120    D)  240	

50.	The weight of bags of potato chips produced by one machine at a packaging plant has a standard deviation of 0.3 oz. A sample of chip bags is to be drawn and the mean weight calculated.  How large must the sample be if the standard deviation of the sampling distribution is to be 0.1 oz.?	
	A)  9 bags    B)  3 bags    C)  6 bags    D)  10 bags	

51.	You are told that the probability of winning the $3 prize in your state's lottery is 1/137. This means:	
A)	if you buy 137 lottery tickets, you will win the $3 prize exactly once.	
B)	if you buy 137,000 lottery tickets, you will win the $3 prize exactly one thousand times.	
C)	if you buy thousands of lottery tickets, the fraction of tickets that will win the $3 prize will be very close to 1/137.	
D)	you will win the $3 prize when you buy your 138th ticket.	

52.	You are told that an event is nearly impossible; it will occur only once in a long sequence of trials. Which of the following probabilities could describe this event?	
	A)  0    B)  .02    C)  .98    D)  1	

53.	A game is played with a pair of tetrahedral (four-sided) dice. Each die has faces numbered 1, 2, 3, and 4. To play, roll the two dice and record the sum of the values on the down faces. What is the probability of rolling a sum of 6?	
	A)  1/2    B)  1/8    C)  3/8    D)  3/16	

54.	Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. How many such passwords are possible?	
	A)  820    B)  468,000    C)  676,000    D)  1,757,600	

55.	Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. A password of this type is chosen at random. What is the probability that the password does not have any vowels?	
	A)  0.20    B)  0.44    C)  0.65    D)  0.85	

56.	A game consists of rolling a regular die. You pay $5 to play the game, and the $5 is not returned. If you roll a 1 or 2, you win $6. If you roll a 3, 4, 5, or 6, you win nothing. What is the mean value for this game, taking into account the $5 cost of the game?	
	A)  –$5    B)  –$3    C)  $1    D)  $3	

57.	A multiple choice quiz has three possible answers for each question. You get 4 points for each correct answer, but you lose 3 points for each incorrect answer. No points are gained or lost if you leave the question blank. What is the mean point value of a random guess on the quiz?	
	A)  1 point    B)  1/3 points    C)  –1/3 points    D)  –2/3 points	

58.	The mean volume of a can of Super Soda is 12 oz., with a standard deviation of 0.6 oz. If the volumes of all cans of Super Soda are normally distributed, 25% of the cans fall below what volume?	
	A)  3 oz.    B)  11.4 oz.    C)  11.6 oz.    D)  12.4 oz.	

59.	The mean volume of a can of Super Soda is 12 oz., with a standard deviation of 0.6 oz. The volumes of all cans of Super Soda are normally distributed. What percent of cans of Super Soda contain less than 10.8 ounces?	
	A)  0.025%    B)  2.5%    C)  0.475%    D)  47.5%	

60.	A math professor notices that the scores from the most recent exam are normally distributed and decides to grade on a curve. The mean score was 60, with a standard deviation of 15. If the professor wants 16% of the students to get an A, what is the minimum score for an A?	
	A)  70    B)  75    C)  80    D)  90	

Answer Key

1.	D	
2.	C	
3.	A	
4.	C	
5.	C	
6.	C	
7.	A	
8.	B	
9.	B	
10.	A	
11.	A	
12.	B	
13.	D	
14.	C	
15.	A	
16.	C	
17.	D	
18.	A	
19.	B	
20.	D	
21.	D	
22.	C	
23.	A	
24.	B	
25.	B	
26.	A	
27.	A	
28.	C	
29.	A	
30.	D	
31.	A	
32.	C	
33.	B	
34.	D	
35.	B	
36.	B	
37.	D	
38.	D	
39.	C	
40.	D	
41.	A	
42.	A	
43.	C	
44.	D	
45.	C	
46.	B	
47.	D	
48.	D	
49.	D	
50.	A	
51.	C	
52.	B	
53.	D	
54.	C	
55.	C	
56.	B	
57.	D	
58.	B	
59.	B	
60.	B