a.
To find: The area under the standard
a.
Answer to Problem 6.1.1RE
The area under the standard normal distribution curve for
Explanation of Solution
Given info:
The z values are 0 and 1.95.
Calculation:
Software procedure:
Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:
- Select Graph > Probability Distribution Plot > View Probability >OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Choose the tab for Shaded Area, then X Value.
- Click the picture for Middle.
- Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The area under the standard normal distribution curve for
b.
To find: The area under the standard normal distribution curve for
b.
Answer to Problem 6.1.1RE
The area under the standard normal distribution curve for
Explanation of Solution
Given info:
The z values are 0 and 0.37.
Calculation:
Software procedure:
Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:
- Select Graph > Probability Distribution Plot > View Probability >OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Choose the tab for Shaded Area, then X Value.
- Click the picture for Middle.
- Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The area under the standard normal distribution curve for
c.
To find: The area under the standard normal distribution curve for
c.
Answer to Problem 6.1.1RE
The area under the standard normal distribution curve for
Explanation of Solution
Given info:
The z values are 1.32 and 1.82.
Calculation:
Software procedure:
Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:
- Select Graph > Probability Distribution Plot > View Probability >OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Choose the tab for Shaded Area, then X Value.
- Click the picture for Middle.
- Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The area under the standard normal distribution curve for
d.
To find: The area under the standard normal distribution curve for
d.
Answer to Problem 6.1.1RE
The area under the standard normal distribution curve for
Explanation of Solution
Given info:
The z values are –1.05 and 2.05.
Calculation:
Software procedure:
Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:
- Select Graph > Probability Distribution Plot > View Probability >OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Choose the tab for Shaded Area, then X Value.
- Click the picture for Middle.
- Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The area under the standard normal distribution curve for
e.
To find: The area under the standard normal distribution curve for
e.
Answer to Problem 6.1.1RE
The area under the standard normal distribution curve for
Explanation of Solution
Given info:
The z values are -0.03 and 0.53.
Calculation:
Software procedure:
Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:
- Select Graph > Probability Distribution Plot > View Probability >OK.
- From Distribution, choose ‘Normal’ distribution.
- Enter the Mean as 0.0 and Standard deviation as 1.0.
- Choose the tab for Shaded Area, then X Value.
- Click the picture for Middle.
- Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The area under the standard normal distribution curve for
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Chapter 6 Solutions
Elementary Statistics: A Step-by-Step Approach with Formula Card
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