State whether the new student’s score increases or decreases the average score.

Question

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Answer 1

Question

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

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Answer 2

Question

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

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Answer 3

Question

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

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Answer 4

Question

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

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Answer 5

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

Answer 6

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

Answer 7

Chapter 2, Problem 27CE

(a)

To determine

State whether the new student’s score increases or decreases the average score.

Answer 8

(a)

Expert Solution

Answer to Problem 27CE

Decrease.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

For 24 students, the average score is 74 points with a standard deviation of 8.9 points.

For one student, who took the make-up the following day, secured 64 points on the exam.

Based on the information, the new student’s score is less than the average of the 24 previous scores.

Therefore, the new score decreases the average score.

Answer 13

(b)

To determine

Obtain the new average.

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

Answer 14

(b)

To determine

Obtain the new average.

Answer 15

(b)

Expert Solution

Answer to Problem 27CE

The new average is 73.5.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

The new average is obtained as given below:

Average={24×Average score+1×Score}Total students in the class={24×74+1×64}(24+1)=1,84025=73.6

Answer 20

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.

Answer 21

(c)

To determine

State whether the new student’s score increases or decreases the standard deviation of the scores.

Answer 22

(c)

Expert Solution

Answer to Problem 27CE

Increase.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Based on the given information, the standard deviation is 8.9 points.

The new mean is decreased in Part (b). In the same way, the standard deviation of the new score is more than one standard deviation away from the mean of 74.