a.
To find: The probability
a.
Answer to Problem 6.1.3RE
The probability using the standard normal distribution is
Explanation of Solution
Given info:
The z values are 0 and 2.07.
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 2.07 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The probability using the standard normal distribution is
b.
To find: The probability
b.
Answer to Problem 6.1.3RE
The probability using the standard normal distribution is
Explanation of Solution
Given info:
The z values are -1.83 and 0.
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 -1.83 for X value1 and then the larger value 0 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The probability using the standard normal distribution is
c.
To find: The probability
c.
Answer to Problem 6.1.3RE
The probability using the standard normal distribution is
Explanation of Solution
Given info:
The z values are -1.59 and 2.01.
Calculation:
Software procedure:
Step by step procedure to find the area under the normal curve between -1.59 and 2.01with 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 -1.59 for X value1 and then the larger value 2.01 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The probability using the standard normal distribution is
d.
To find: The probability
d.
Answer to Problem 6.1.3RE
The probability using the standard normal distribution is
Explanation of Solution
Given info:
The z values are 1.33 and 1.88.
Calculation:
Software procedure:
Step by step procedure to; find the area under the normal curve between 1.33 and 1.88with 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 1.33 for X value1 and then the larger value 1.88 for the X value2.
- Click OK.
Output using the MINITAB software is given below:
Therefore,
Conclusion:
The probability using the standard normal distribution is
e.
To find: The probability
e.
Answer to Problem 6.1.3RE
The probability using the standard normal distribution is
Explanation of Solution
Given info:
The z values are -2.56 and 0.37.
Calculation:
Software procedure:
Step by step procedure to; find the area under the normal curve between -2.56 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 −2.56 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 probability using the standard normal distribution is
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Chapter 6 Solutions
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