Consider the normal distribution represented by the normal curve in Fig 17-12 . Assume that P is a point of inflection of the curve. Figure 17-12 a. Find the mean μ of the distribution. b. Find the median M of the distribution. c. Find the standard deviation σ of the distribution.

Question

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Answer 1

Textbook Question

Chapter 17, Problem 1E

Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a point of inflection of the curve.

Chapter 17, Problem 1E, Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a

Figure 17-12

a. Find the mean μ of the distribution.

b. Find the median M of the distribution.

c. Find the standard deviation σ of the distribution.

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.

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

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Answer 2

Textbook Question

Chapter 17, Problem 1E

Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a point of inflection of the curve.

Chapter 17, Problem 1E, Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a

Figure 17-12

a. Find the mean μ of the distribution.

b. Find the median M of the distribution.

c. Find the standard deviation σ of the distribution.

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.

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

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Answer 3

Textbook Question

Chapter 17, Problem 1E

Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a point of inflection of the curve.

Chapter 17, Problem 1E, Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a

Figure 17-12

a. Find the mean μ of the distribution.

b. Find the median M of the distribution.

c. Find the standard deviation σ of the distribution.

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.

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

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Answer 4

Textbook Question

Chapter 17, Problem 1E

Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a point of inflection of the curve.

Chapter 17, Problem 1E, Consider the normal distribution represented by the normal curve in Fig 17-12. Assume that P is a

Figure 17-12

a. Find the mean μ of the distribution.

b. Find the median M of the distribution.

c. Find the standard deviation σ of the distribution.

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.

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

Answer 8

Expert Solution

To determine

(a)

To find:

The mean μ of the distribution.

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

To find:

The mean μ of the distribution.

Answer 13

Answer to Problem 1E

Solution:

The mean μ of the distribution is 80 lb.

Answer 14

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 1

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the mean μ of the distribution is μ=80 lb.

Conclusion:

The mean μ of the distribution is 80 lb.

Answer 15

Expert Solution

To determine

(b)

To find:

The median M of the distribution.

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

(b)

To find:

The median M of the distribution.

Answer 20

Answer to Problem 1E

Solution:

The median M of the distribution is 80 lb.

Answer 21

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 2

With P as a point of inflection of the curve.

Definition:

The point of intersection of the horizontal (data) axis and the line of symmetry of the normal curve, the center of the distribution. The center corresponds to both the median and mean of the distribution.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

This implies that the median M of the distribution.is 80 lb.

Conclusion:

The median M of the distribution is 80 lb.

Answer 22

Expert Solution

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

(c)

To find:

The standard deviation σ of the distribution.

Answer 27

Answer to Problem 1E

Solution:

The standard deviation σ of the distribution is 10 lb.

Answer 28

Explanation of Solution

Given:

The normal distribution curve is,

Excursions in Modern Mathematics (9th Edition), Chapter 17, Problem 1E , additional homework tip 3

With P as a point of inflection of the curve.

Definition:

The standard deviation of the normal distribution is the horizontal distance between the axis of symmetry of the curve and one of the two points of inflection.

Calculation:

From the given figure, it is seen that the point of intersection of the horizontal axis and the line of symmetry is at 80 lb.

The point of inflection of the curve is 90 lb.

Therefore the distance between the point of inflection and the line of symmetry is,

90−80=10 lb.

This implies that the standard deviation σ of the distribution.is 10 lb.

Conclusion:

The standard deviation σ of the distribution.is 10 lb.