Concept explainers
Given that z is a standard normal random variable, find z for each situation.
- a. The area to the left of z is .2119.
- b. The area between –z and z is .9030.
- c. The area between –z and z is .2052.
- d. The area to the left of z is .9948.
- e. The area to the right of z is .6915.
a.
Find the value of z.
Answer to Problem 15E
The value of z is –0.80.
Explanation of Solution
Calculation:
The area to the left of z is given as 0.2119.
The area to the left of z, which is 0.2119 can be written as
z value:
Software Procedure:
Step-by-step procedure to obtain the z using the EXCEL:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORMSINV(0.2119) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Hence,
Thus, the value of z is –0.80.
b.
Obtain the value of z.
Answer to Problem 15E
The value of z is 1.66.
Explanation of Solution
Calculation:
The area between –z and z is given as 0.9030.
Thus, the area between –z and z, which is 0.9030 can be written as,
z value:
Software Procedure:
Step-by-step procedure to obtain the z using the EXCEL:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORMSINV(0.9515) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Hence,
Thus, value of z is 1.66.
c.
Compute the value of z.
Answer to Problem 15E
The value of z is 0.26.
Explanation of Solution
Calculation:
The area between –z and z is given as 0.2052.
Thus, the area between –z and z, which is 0.2052 can be written as,
z value:
Software Procedure:
Step-by-step procedure to obtain the z using the EXCEL:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORMSINV(0.6026) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Hence,
Thus, value of z is 0.26.
d.
Calculate the value of z.
Answer to Problem 15E
The value of z is 2.56.
Explanation of Solution
Calculation:
The area to the left of z is given as 0.9948.
The area to the left of z, which is 0.9948 can be written as
z value:
Software Procedure:
Step-by-step procedure to obtain the z using the EXCEL:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORMSINV(0.9948) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Hence,
Thus, the value of z is 2.56.
e.
Compute the value of z.
Answer to Problem 15E
The value of z is –0.50.
Explanation of Solution
Calculation:
The area to the right of z is given as 0.6915.
Thus, the area to the right of z, which is 0.6915, can be written as,
z value:
Software Procedure:
Step-by-step procedure to obtain the z using the EXCEL:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORMSINV(0.3085) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Hence,
Thus, value of z is –0.50.
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Chapter 6 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
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