To graph: The normal curve.

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 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

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Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, (which is identical to a standard gamma distribution with α = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) the expected time between two successive arrivals (b) the standard deviation of the time between successive arrivals (c) P(X ≤ 1) (d) P(2 ≤ X ≤ 4) You may need to use the appropriate table in the Appendix of Tables

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 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

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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 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

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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 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

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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 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

Answer 6

Chapter 1.4, Problem 105E

(a)

To determine

To graph: The normal curve.

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

Answer 7

Chapter 1.4, Problem 105E

(a)

To determine

To graph: The normal curve.

Answer 8

(a)

Expert Solution

Explanation of Solution

Graph: The normal curve can be obtained by using the Minitab software. Follow the steps given below:

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Graph and then select the option ‘probability distribution plot.’ Then, select View single. Click on Ok.

Step 3: Enter the value of 288 in mean and 32 in standard deviation, and click on Ok.

The normal curve can be obtained as:

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 1

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

Answer 13

(b)

To determine

To find: The table for values of scores corresponds to the standard deviation from the mean.

Answer 14

(b)

Expert Solution

Answer to Problem 105E

Solution: The table can be shown below:

	Lower limit	Upper limit
288±32	256	320
288±2×32	224	352
288±3×32	192	384

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

Explanation of Solution

Calculation: The table corresponding to values of scores for the standard deviation deviating from mean can be seen as below:

	Lower limit	Upper limit
μ±σ=288±32	μ−σ=288−32=256	μ+σ=288+32=320
μ±2σ=288±(2×32)	μ−2σ=288−(2×32)=224	μ+2σ=288+(2×32)=352
μ±3σ=288±(3×32)	μ−3σ=288−(3×32)=192	μ+3σ=288+(3×32)=384

Answer 19

To determine

To graph: The sketch for the points calculated above.

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

Answer 20

To determine

To graph: The sketch for the points calculated above.

Answer 21

Expert Solution

Explanation of Solution

The lower limits and upper limits were calculated above.

Graph: The sketch of these points can be made using the 68−95−99.7 rule.

Introduction to the Practice of Statistics, Chapter 1.4, Problem 105E , additional homework tip 2

Answer 22

Expert Solution

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

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 reading score value for the students can be obtained by the steps below:

Step 1: For calculating 68% of data,

μ±σ=(μ−σ,μ+σ)=(288−32,288+32)=(256,320)

Step 2: For calculating 95% of data,

μ±2σ=(μ−2σ,μ+2σ)=(288−64,288+64)=(224,352)

Step 3: For calculating 99.7% of data,

μ±3σ=(μ−3σ,μ+3σ)=(288−96,288+96)=(192,384)

Answer 26

(c)

To determine

To find: The range of reading scores using the 68−95−99.7 rule.

Answer 27

(c)

Expert Solution

Answer to Problem 105E

Solution: The range of reading scores are (256,320)_, (224,352)_, and (192,384)_.

Answer 28

(c)

Expert Solution

Answer 29

(c)

Expert Solution

Answer 30

Expert Solution

Answer 31

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).