Deck 7: Understanding Statistics and Probability

Question 1

The number of seats occupied per flight on a jet for 16 trans-Atlantic flights was recorded. The numbers were 302 , 424 , 387 , 418 , 403 , 350 , 366 , 313 , 411 , 391 , 328 , 408 , 402 , 382 , 413 , and 398 . Calculate the mean, the median, and the mode of the number of seats occupied per flight.

A) Mean: 387.75 seats; median: 394.5 seats; mode: no mode
B) Mean: 381 seats; median: 394.5 seats; mode: no mode
C) Mean: 394.5 seats; median: 394.5 seats; mode: 387.75 seats
D) Mean: 381 seats; median: 387.75 seats; mode: 394.5 seats
E) Mean: 387.75 seats; median: 394.5 seats; mode: 381 seats

Answer 1

Mean: 381 seats; median: 394.5 seats; mode: no mode

Question 2

The bar graph below shows the regions in which all the passenger cars were produced during a recent year. What is the difference between the number of passenger cars produced in Western Europe and the number produced in Eastern Europe/Russia?

A) 24 million passenger cars
B) 7 million passenger cars
C) 11 million passenger cars
D) 10 million passenger cars
E) 23 million passenger cars

Answer 2

7 million passenger cars

Question 3

Compute Malcolm's GPA, to the nearest hundredth, for the semester (A=4, B=3, C=2, D=1, F=0).

A) 0.77
B) 2.85
C) 1.00
D) 3.08
E) 3.25

Answer 3

2.85

Question 4

A tire company tested a particular model of super radial tire and found the tires to be normally distributed with respect to wear. The "average" (mean) tire wore out at 44,000 miles, and the standard deviation was 6,500 miles. Approximately what percent of the tires are likely to wear out before 36,200 miles? ​

A) 33 %
B) 28 %
C) 23 %
D) 3 %
E) 13 %

Question 5

Wendy took a standardized test that consisted of five different parts. Her score on each part, as well as the respective means and standard deviations are displayed in the table below. On which test part did she do the "best"?

A) Vocabulary
B) Reading Comprehension
C) Algebra
D) Logic
E) Arithmetic

Question 6

Joe has a 2.79 GPA after 39 credits. He says that he has a total of 108.81 grade points. Julie says that's impossible. Who is correct, and why? ​

A) Julie, because .
B) Joe, because credits must be greater than GPA
C) Julie, because grade points must be a whole number
D) Julie, because credits must be greater than grade points
E) Joe, because .

Question 7

Eight health maintenance organizations (HMOs) presented group health insurance plans to a company. The monthly rates per employee were $422, $394, $406, $399, $425, $356, $403, and $427. Calculate the mean and the median monthly rates for these eight HMOs.

A) Mean: $404; median: $404
B) Mean: $404; median: $404.5
C) Mean: $404.5; median: $404
D) Mean: $404.5; median: $404.5
E) Mean: $808; median: $404.5

Question 8

The number of big-screen televisions sold each month for 1 year was recorded by an electronics store. The results were 18 , 15 , 24 , 24 , 21 , 19 , 27 , 29 , 19 , 24 , 18 , and 38 . Calculate the mean, the median, and the mode of the number of televisions sold per month.

A) Mean: 22.5 TVs; median: 24 TVs; mode: 23 TVs
B) Mean: 22.5 TVs; median: 22.5 TVs; mode: 24 TVs
C) Mean: 23 TVs; median: 23 TVs; mode: 22.5 TVs
D) Mean: 23 TVs; median: 22.5 TVs; mode: 24 TVs
E) Mean: 23 TVs; median: 24 TVs; mode: 22.5 TVs

Question 9

Beatrice has a 2.60 GPA after completing 117 credits. In her final semester of school she is taking 15 credit hours. If she wants to graduate with at least a 2.44 GPA, what is the minimum GPA she must make in her final semester?

A) 2.58
B) 2.28
C) 3.85
D) 1.19
E) 2.40

Question 10

The table below shows the age of the winners of the Clark County Innovation Award, given annually to a member of the community for the best invention, for the years 1960 through 1989. Construct a stem-and-leaf plot to display this data.

A)
B)
C)
D)
E)

Question 11

The table below shows the immigration rates in thousands by decade, from 1900 to 1990, of a small European country. Construct a line graph to display this data.

A)
B)
C)
D)
E)

Question 12

The following table shows the highest education attainment levels for adults in the United States for a given year. Construct a circle graph to display this data.

A)
B)
C)
D)
E)

Question 13

The line graph below shows the average monthly snowfall during ski season around Aspen, Colorado. During which month is the snowfall the greatest ? ​ ​

A) November
B) October
C) April
D) January
E) February

Question 14

The following table shows the population of a state's eight most populated cities. Construct a bar graph to display this data.

A)
B)
C)
D)
E)

Question 15

A consumer research group purchased identical items in eight grocery stores. The costs for the purchased items were $ 46.03 , $ 52.17 , $ 41.62 , $ 40.85 , $ 48.81 , $ 42.64 , $ 47.91 , and $ 45.97 . Calculate the mean and the median costs of the purchased items. Round your answers to four decimal places. ​

A) Mean: $ 45.7500 ; median: $ 45.7500
B) Mean: $ 52.2857 ; median: $ 46.0000
C) Mean: $ 46.0000 ; median: $ 46.0000
D) Mean: $ 45.7500 ; median: $ 46.0000
E) Mean: $ 46.0000 ; median: $ 45.7500

Question 16

The data below represents the distance, in miles, that a class of students lives from the school. Calculate the mode for this group of data.

A) 22
B) 19
C) 27
D) 20
E) 17

Question 17

The table below shows the breakdown of International Arms Sales per country for a particular year. Construct a circle graph using the % of Total data.

A)
B)
C)
D)
E)

Question 18

The bar graph below shows the regions in which all the passenger cars were produced during a recent year. What percent of the passenger cars were produced in Latin America? Round your answer to the nearest percent.

A) 21 %
B) 28 %
C) 38 %
D) 5 %
E) 8 %

Question 19

The line graph below shows the average monthly snowfall during ski season around Aspen, Colorado. What is the average snowfall during March? ​ ​

A) 19 inches
B) 17 inches
C) 16 inches
D) 15 inches
E) 20 inches

Question 20

Belinda took three tests. If her median score was 55 , her mean score was 66 , and the range was 39 , what were her three test scores?

A) 47 , 66 , 85
B) 27 , 55 , 66
C) 36 , 55 , 74
D) 52 , 55 , 91
E) 55 , 66 , 94

Question 21

How many ways are there to arrange 3 students in a row of seats?

A) 12
B) 9
C) 27
D) 3
E) 6

Question 22

On a certain exam, Charles corrected 12 papers and found the mean for his group to be 76 . Beth corrected the remaining 19 papers and found that the mean for her group was 51 . What is the mean of the combined group of students, rounded to the nearest whole number? ​

A) 51
B) 76
C) 66
D) 61
E) 64

Question 23

A class of college students collected data about how many siblings they had and how many siblings their mother had. Calculate the standard deviation for the students' number of siblings.

A) 2.49
B) 2.03
C) 2.67
D) 1.56
E) 2.25

Question 24

A bag contains 10 colored beads. A bead is selected from the bag and then replaced. After five draws, a red bead has been pulled out three times, a blue bead once , and a green bead once . Which statement about the contents of the bag must be true?

A) There are six red beads in the bag.
B) There is at least one green bead in the bag.
C) There are no yellow beads in the bag.
D) There are at least three red beads in the bag.
E) There are two blue beads in the bag.

Question 25

A multiple choice quiz consists of 10 questions, each with 4 answer choices. What is the total number of ways that the questions can be answered on the quiz?

A) 40
B) 1,048,576
C) 5,040
D) 210
E) 10,000

Question 26

In a special triathlon, Denita swam 1 mile in 20 minutes, biked 25 miles in 50 minutes, and then ran 5 miles in 50 minutes. What was her "average" speed in miles/hour for the race, to the nearest tenth?

A) 30.0 miles/hour
B) 13.0 miles/hour
C) 3.0 miles/hour
D) 6.0 miles/hour
E) 15.5 miles/hour

Question 27

Drawing from a regular deck of playing cards, what is the probability of drawing a face card (jack, queen, or king) 4 times in a row, with replacement? ​

A) 0.0028
B) 0.0123
C) 0.2308
D) 0.0833
E) 0.0144

Question 28

How many ways can 6 flags be arranged on a flag pole, one above the other, if there are 8 different flags to choose from?

A) 64
B) 20,160
C) 262,144
D) 36
E) 28

Question 29

Tiles with each of the 26 letters of the alphabet printed on them are placed in a box. If five tiles are selected from the box, with replacement, what is the probability that the tiles selected will spell the word COUCH? The letters must be selected in the correct order. ​

A)
B)
C)
D)
E)

Question 30

Below are the annual salaries (in thousands of dollars) of workers in Wilson Widget factory: 20 , 20 , 23 , 23 , 23 , 25 , 25 , 25 , 25 , 28 , 28 , 28 , 29 , 29 , 29 , 32 , 32 , 33 , 36 , 40 , 40 , 65 Which measure of central tendency should you use to describe the average salary?

A) standard deviation, since most of the salaries are close together
B) mode, since there are many identical salaries
C) range, since there are more than 15 salaries
D) mean, since there are less than 50 salaries
E) median, since there is an outlying salary

Question 31

An oil company is trying to decide if it will be worth their money to drill a well in a certain area. They determine that it will cost $125,000 to drill the well. The three possible outcomes of the drilling are a dry well, a "medium" strike that would produce about $700,000, and a big strike that would produce about $1,250,000. The company has estimated that the probability of a "medium" strike is 1/10 and the probability of a big strike is 1/22. What is the oil company's expected value for drilling a well in this area?

A) $31,818.18
B) $1818.18
C) -$126,818.18
D) $116,401.52
E) -$108,636.36

Question 32

A game of chance at the carnival costs $4 to play. The player picks a number between 1 and 6 and then three dice are rolled. If the number picked shows on all three dice the player wins $19. If the number picked shows on two of the dice then the player wins $13. If the number shows up once, $9 is won, and if it doesn't show up at all the player owes another $4. What is the player's expected value for this game?

A) -$2.20
B) -$0.51
C) -$3.77
D) $4.67
E) $8.67

Question 33

family of 7 decides that each member will be responsible for buying a gift for only one other family member. If the names of all the members are put in a dish and everybody selects one name, what is the probability of every family member selecting his or her own name? ​

A)
B)
C)
D) ​
E)

Question 34

The heights of 1100 boys at West High School were measured, and the mean was found to be 74 inches, with a standard deviation of 2.7 inches. If the heights are approximately normally distributed, what range of heights will include 95% of the boys? ​

A) 70.3 and 77.7 inches tall
B) 69.1 and 78.9 inches tall
C) 71.4 and 76.6 inches tall
D) 68.6 and 79.4 inches tall
E) 71.3 and 76.7 inches tall

Question 35

A hospital nursery with 22 babies contains exactly 11 girls and 11 boys. If the chances of a woman giving birth to a boy or a girl are the same, what is the probability that exactly 11 out of the 22 babies are girls? ​

A) 0.3364
B) 0.0455
C) 0.1682
D) 0.5000
E) 0.0107

Question 36

In a family of 5 children, what is the probability of having 3 girls and 2 boys?

A) 0.2500
B) 0.1250
C) 0.6250
D) 0.2000
E) 0.3125

Question 37

A school is having a carnival to raise funds. One of the games requires the player to pay $2 and spin the spinner. The player wins the amount of money in the section where the pointer stops. If 1000 people play the game, how much money can the school expect to make?

A) $375.00
B) $160.00
C) $1250.00
D) $1625.00
E) $2000.00

Question 38

Suppose the distribution of heights of a group of 400 children is normal, with a mean of 100 centimeters and a standard deviation of 20 centimeters. About how many of these children are taller than 100 centimeters?

A) 272
B) 50
C) 400
D) 336
E) 200

Question 39

A drawer has 10 red socks and 10 blue socks. If 3 socks are selected from the drawer, without replacement, what is the probability that they will all be the same color?

A) 0.3000
B) 0.0225
C) 0.1500
D) 0.2105
E) 0.1667

Question 40

Let's say a student scored 33 on a math achievement test for which the mean was 43 and the standard deviation was 10. Judging on the basis of this performance, what score would you predict for her on a standardized test for which the mean is 100 and the standard deviation 14?

A) 114
B) 77
C) 86
D) 110
E) 90

Question 41

A group of 3 children are each to choose one popsicle from a box of 6 : 2 grape, 2 cherry, and 2 orange. What is the probability that each child will get the flavor they want? ​

A) 0.8889
B) 0.8333
C) 0.6667
D) 0
E) 1

Question 42

It costs $2.75 to play a dice game at the fair. The player rolls two standard dice and forms a proper fraction with the two numbers that are rolled. If the number represented by the fraction is in simplest form the player wins, if it is reducible he loses. How much should a winning roll pay out in order to make the game fair? Note: Fractions such as 2/2 are reducible to whole numbers.

A) $2.75
B) $4.50
C) $1.75
D) $5.25
E) $1.64

Question 43

An ice cream store offers 29 different flavors of ice cream. How many triple-scoop ice cream cones are possible if each scoop must be a different flavor and the flavors can be in any order?

A) 21924
B) 24389
C) 3654
D) 87
E) 754

Question 44

The Math Club has 13 members. How many different ways can 4 of the members be selected to attend a conference?

A) 715
B) 17,160
C) 28,561
D) 286
E) 52

Question 45

The following dates all have a similar pattern, the month and the day multiply to give the last two digits of the year. 6/12/72 3/25/75 5/19/95 In which of the five years below will such dates be most probable? 1924 1937 1973 1974 1988

A) 1937
B) 1988
C) 1973
D) 1924
E) 1974

Question 46

Suppose you are designing two dice which will be rolled and the face values added together. Which combination of numbers should be displayed on the faces of the two dice to yield only even sums where each sum is equally likely?

A) Die #1: 6, 4, 6, 4, 6, 4 Die #2: 9, 3, 9, 3, 9, 3
B) Die #1: 6, 4, 3, 6, 4, 3 Die #2: 6, 4, 3, 6, 4, 3
C) Die #1: 1, 9, 3, 1, 9, 3 Die #2: 1, 9, 3, 1, 9, 3
D) Die #1: 1, 3, 1, 3, 1, 3 Die #2: 9, 7, 9, 7, 9, 7
E) Die #1: 1, 9, 1, 9, 1, 9 Die #2: 3, 7, 3, 7, 3, 7

Question 47

Each of the letters of the word MISSISSIPPI is written on a card, and the cards are placed in a hat. One card is drawn at random from the hat. a. What is the probability that the card has the letter I on it? b. Which is greater, the probability of choosing a letter M or that of choosing a letter S? ​

A) (a) (b) Choosing a letter M
B) (a) (b) Choosing a letter M
C) (a) (b) Choosing a letter S
D) (a) (b) Choosing a letter S
E) (a) (b) Neither

Question 48

What is the minimum number of people who would have to be enrolled in a school to guarantee that there were at least two students who have the same birthday (excluding year) and the same last initial ?

A) 9,909
B) 9,516
C) 9,490
D) 9,517
E) 9,491

Question 49

The Midway Cafe is offering a three-course meal at a special price. You can choose among the following options for the special: Appetizer: soup or salad Main Course: lasagna, beef tips, fried chicken, pork chops Dessert: carrot cake, cherry pie, ice cream If there are 5 choices of salad dressing and 3 choices of ice cream, how many dinner combinations are possible?

A) 168
B) 60
C) 360
D) 24
E) 120

Question 50

What is the probability of rolling a 4 on a standard die 3 times in a row? ​

A)
B)
C)
D)
E)

Question 51

If two cards are selected from a standard deck of playing cards, without replacement, what is the probability of getting two face cards? ​

A)
B)
C)
D)
E)

Question 52

Two dice are rolled. ​ a. What is the probability that the sum of the dots on the upward faces is 2? b. What is the probability that the sum of the dots on the upward faces is 14? c. What is the probability that the sum of the dots on the upward faces is less than 15? d. What is the probability that the sum of the dots on the upward faces is 6? ​

A) (a) ; (b) 0; (c) 1; (d)
B) (a) ; (b) 1; (c) 0; (d)
C) (a) ; (b) 1; (c) 0; (d)
D) (a) ; (b) 0; (c) 1; (d)
E) (a) ; (b) 1; (c) 0; (d)

Question 53

How can be written using factorials? ​

A)
B)
C)
D)
E)

Question 54

How many different five-letter arrangements can be made using the letters in the word algebra?

A) 2520
B) 5040
C) 1260
D) 21
E) 42

Question 55

Suppose the American Lung Association states that approximately 1 out of every 24 deaths in the United States last year was from lung cancer. If there are 72 students in a class, how many would you expect to die from lung cancer?

A) 6
B) 1
C) 48
D) 3
E) 0