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.
Want to see more full solutions like this?
Chapter 6 Solutions
MindTap Business Statistics with XLSTAT, 1 term (6 months) Printed Access Card for Anderson/Sweeney/Williams/Camm/Cochran's Modern Business Statistics ... Office Excel, 6th (MindTap Course List)
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman