The distribution using 68 − 95 − 99.7 rule.

Question

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Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

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Answer 5

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

Answer 6

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

Answer 7

Chapter 1.4, Problem 110E

(a)

To determine

To find: The distribution using 68−95−99.7 rule.

Answer 8

(a)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are (7856, 20,738)_, (1415, 27,179)_, and (−5026, 33,620)_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,297−6441, 14,297+6441)=(7856, 20,738)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,297−(2×6441), 14,297+(2×6441))=(1415, 27,179)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,297−(3×6441), 14,297+(3×6441))=(−5026, 33,620)

Answer 13

(b)

To determine

Whether the above rule is applicable or not.

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

Answer 14

(b)

To determine

Whether the above rule is applicable or not.

Answer 15

(b)

Expert Solution

Answer to Problem 110E

Solution: This rule is not applicable.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is giving negative values and words spoken cannot be negative. Therefore, the normal distribution cannot be used in this case. This rule is applicable only when the data has a normal distribution.

Answer 20

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

Answer 21

(c)

To determine

To find: The distribution using 68−95−99.7 rule.

Answer 22

(c)

Expert Solution

Answer to Problem 110E

Solution: The calculated values are obtained as (5004, 23,116)_, (−4052, 32,172)_, and (−13,108, 41,228)_.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation: The 68−95−99.7 rule states that in the normal distribution, 68% of data falls under (μ±σ), 95% of the data falls under (μ±2σ), and 99.7% of the data falls under (μ±3σ).

With the given values of mean and standard deviation, the range of the number of words can be obtained by the following steps:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(14,060−9056, 14,060+9056)=(5004, 23,116)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(14,060−(2×9056), 14,060+(2×9056))=(−4052, 32,172)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(14,060−(3×9056), 14,060+(3×9056))=(−13,108, 41,228)

Answer 27

To determine

Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

Answer 28

To determine

Whether the above rule is applicable or not.

Answer 29

Expert Solution

Answer to Problem 110E

Solution: This rule is also not applicable.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

From the above calculation, it is clear that this rule is not applicable here because it is also providing negative values, which cannot be possible.

Answer 34

(d)

To determine

Whether the data supports conventional wisdom or not.

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.

Answer 35

(d)

To determine

Whether the data supports conventional wisdom or not.

Answer 36

(d)

Expert Solution

Answer to Problem 110E

Solution: The data does not support conventional wisdom.

Answer 37

(d)

Expert Solution

Answer 38

(d)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

It can be seen from the question that the mean number of words spoken per day by the women is greater than the mean number of words spoken per day by the men and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of number of words spoken for women than men.