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 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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.

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

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Students have asked these similar questions

Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6. a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…

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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 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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.

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

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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 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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.

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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.

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 1.4, Problem 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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.

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

Answer 6

Chapter 1.4, Problem 119E

(a)

To determine

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

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

Answer 7

Chapter 1.4, Problem 119E

(a)

To determine

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

Answer 8

(a)

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (8489, 20,919)_, (2274, 27,134)_, and (−3941, 33,349)_.

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)=(14,704−6215, 14,704+6215)=(8489, 20,919)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(14,704−(2×6215), 14,704+(2×6215))=(2274, 27,134)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(14,704−(3×6215), 14,704+(3×6215))=(−3941, 33,349)

Answer 13

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

Answer 14

To determine

To explain: Whether the above rule is applicable or not.

Answer 15

Expert Solution

Answer to Problem 119E

Solution: This rule is not applicable.

Answer 16

Expert Solution

Answer 17

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. The normal distribution cannot be used in the provided case. This rule is applicable only in the case of normal distribution.

Answer 20

To determine

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

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

Answer 21

To determine

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

Answer 22

Expert Solution

Answer to Problem 119E

Solution: The calculated values are (7158, 22,886)_, (−706, 30,750)_, and (−8570, 38,614)_.

Answer 23

Expert Solution

Answer 24

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 scores for the students can be obtained by the following steps shown below:

Step 1: For calculating 68% of data,

(μ±σ)=(μ−σ,μ+σ)=(15,022−7864, 15,022+7864)=(7158, 22,886)

Step 2: For calculating 95% of data,

(μ±2σ)=(μ−2σ,μ+2σ)=(15,022−(2×7864), 15,022+(2×7864))=(−706, 30,750)

Step 3: For calculating 99.7% of data,

(μ±3σ)=(μ−3σ,μ+3σ)=(15,022−(3×7864), 15,022+(3×7864))=(−8570, 38,614)

Answer 27

To determine

To explain: Whether the above rule is applicable or not.

Expert Solution

Answer to Problem 119E

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

To explain: Whether the above rule is applicable or not.

Answer 29

Expert Solution

Answer to Problem 119E

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

To determine

To explain: Whether the data supports conventional wisdom or not.

Expert Solution

Answer to Problem 119E

Solution: 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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

Answer 35

To determine

To explain: Whether the data supports conventional wisdom or not.

Answer 36

Expert Solution

Answer to Problem 119E

Solution: Data does not support conventional wisdom.

Answer 37

Expert Solution

Answer 38

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 men is greater than the mean number of words spoken per day by the women, and the standard deviation of women is less than the standard deviation of men. There is a more concentrated distribution of the number of words spoken by women than men.

Answer 41

(b)

To determine

To explain: The conclusion from the observation.

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.

Answer 42

(b)

To determine

To explain: The conclusion from the observation.

Answer 43

(b)

Expert Solution

Answer to Problem 119E

Solution: Both men and women from Mexico tend to speak more than those from United states.

Answer 44

(b)

Expert Solution

Answer 45

(b)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

The mean for both men and women is higher for the Mexican study as compared to U.S. study. It shows that both men and women from Mexico tend to speak more than those from the United States.