Question 1

How many ways are there to arrange 3 students in a row of seats?
A) 12
B) 9
C) 27
D) 3
E) 6

Accepted Answer

There are 3 choices for the first seat, 2 choices for the second seat (since one student is already seated), and 1 choice for the last seat. So the total number of arrangements is 3 x 2 x 1 = 6. Therefore, the correct answer is E.

Question 2

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

Accepted Answer

To find the mean of the combined group, calculate the total points for both groups and divide by the total number of papers. For Charles: 12 papers * 76 points = 912 points. For Beth: 19 papers * 51 points = 969 points. Combined: 912 + 969 = 1881 points for 31 papers. Mean = 1881 / 31 ≈ 61.

Question 3

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

Accepted Answer

The answer of A class of college students collected data...

Question 4

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.

Accepted Answer

The fact that a green bead was drawn at least once proves that there is at least one green bead in the bag.

Question 5

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

Accepted Answer

For each question, there are 4 possible answer choices. Since there are 10 questions, we can multiply the number of possibilities for each question together to get the total number of ways the quiz can be answered. This gives us 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^10 = 1,048,576. Therefore, the correct answer is B.

Question 6

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

Accepted Answer

To find the average speed, we need to calculate the total distance and the total time, and then divide total distance by total time.

Total distance = 1 mile (swim) + 25 miles (bike) + 5 miles (run) = 31 miles
Total time = 20 minutes (swim) + 50 minutes (bike) + 50 minutes (run) = 120 minutes or 2 hours

Average speed = Total distance / Total time = 31 miles / 2 hours = 15.5 miles/hour (to the nearest tenth)

Therefore, the best choice is E.

Question 7

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

Accepted Answer

The probability of drawing a face card (jack, queen, or king) from a regular deck is 12/52 (since there are 12 face cards out of 52 total cards). With replacement means each draw is independent, so the probability of drawing a face card 4 times in a row is (12/52)^4 = 0.0028.

Question 8

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

Accepted Answer

There are 8 choices for the first flag, 7 choices for the second flag, 6 choices for the third flag, and so on until there are only 3 choices for the sixth and final flag. Therefore, the total number of arrangements is 8 x 7 x 6 x 5 x 4 x 3 = 20,160.

Question 9

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)

Accepted Answer

The answer of Tiles with each of the 26 letters...

Question 10

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

Accepted Answer

The median is the best measure of central tendency to use in this case because there is an outlier (the salary of 65 thousand dollars) that would skew the mean, making it not representative of the typical salary. The median, being the middle value when the data is ordered, is not affected by outliers and thus provides a better central value for the data set.

Question 11

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

Accepted Answer

The answer of An oil company is trying to decide...

Question 12

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

Accepted Answer

The expected value is the sum of the probabilities of each outcome multiplied by the value of that outcome. The probability of winning $19 is 1/216, the probability of winning $13 is 3/216, the probability of winning $9 is 6/216, and the probability of losing $4 is 206/216. So the expected value is (1/216) * $19 + (3/216) * $13 + (6/216) * $9 + (206/216) * -$4 = -$2.20.

Question 13

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)

Accepted Answer

The answer of family of 7 decides that each member...

Question 14

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

Accepted Answer

The answer of The heights of 1100 boys at West...

Question 15

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

Accepted Answer

The probability of having a girl or a boy is 1/2 or 0.5. The number of ways to choose 11 girls out of 22 babies is given by the combination formula: 
C(22, 11) = 22! / (11! 11!) = 22 x 21 x 20 x ... x 12 / 11 x 10 x 9 x ... x 2 x 1 = 42,504
The total number of outcomes or ways to have any 11 babies out of 22 is also given by the combination formula: 
C(22, 11) = 22! / (11! 11!) = 42,504
Therefore, the probability of having exactly 11 girls out of 22 babies is:
C(11, 22) x (1/2)^22 = 42,504 x 0.5^22 = 0.1682 (rounded to four decimal places)
Therefore, the best answer choice is C.

Question 16

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

Accepted Answer

The total number of possible combinations of children in a family of 5 is 2^5=32 (2 choices for each child). The number of ways to have 3 girls and 2 boys can be calculated using the binomial coefficient formula: C(5,3) = 10. Therefore, the probability of having 3 girls and 2 boys is 10/32 = 0.3125.

Question 17

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

Accepted Answer

The answer of A school is having a carnival to...

Question 18

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

Accepted Answer

In a normal distribution, the mean divides the distribution in half, so approximately 50% of the values lie above the mean. Since there are 400 children, about 50% of 400, which is 200 children, are taller than 100 centimeters.

Question 19

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

Accepted Answer

The total number of ways to select 3 socks from 20 is (20 choose 3) = 1140.

To select 3 socks all of the same color, either all 3 red or all 3 blue, there are (10 choose 3) + (10 choose 3) = 240 + 240 = 480 ways.

Thus, the probability of selecting 3 socks all of the same color is 480/1140 = 0.2105.

Therefore, the best choice is D.

Question 20

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

Accepted Answer

The student's score is 1 standard deviation below the mean on the math achievement test (43 - 33 = 10, which is the standard deviation). To predict her score on the standardized test, we apply the same position relative to the mean, which is 1 standard deviation below the mean of 100. Since the standard deviation of the standardized test is 14, her predicted score would be 100 - 14 = 86.

Quiz 7: Understanding Statistics and Probability

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

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 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 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 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?

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?

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? ​

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?

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. ​

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?

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? ​

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 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? ​

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

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?

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 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?

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?

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?

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?

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.

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?

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 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?