Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Textbook Question
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Chapter 6.2, Problem 15E

Given that z is a standard normal random variable, find z for each situation.

  1. a. The area to the left of z is .2119.
  2. b. The area between –z and z is .9030.
  3. c. The area between –z and z is .2052.
  4. d. The area to the left of z is .9948.
  5. e. The area to the right of z is .6915.

a.

Expert Solution
Check Mark
To determine

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 P(Zz)=0.2119.

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:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 6.2, Problem 15E , additional homework tip  1

Hence, P(Z0.80)=0.2119.

Thus, the value of z is –0.80.

b.

Expert Solution
Check Mark
To determine

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,

P(zZz)=0.9030P(Zz)P(Zz)=0.9030P(Zz)[1P(Zz)]=0.90302P(Zz)1=0.9030P(Zz)=1+0.90302P(Zz)=1.9032P(Zz)=0.9515

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:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 6.2, Problem 15E , additional homework tip  2

Hence, P(Z1.66)=0.9515.

Thus, value of z is 1.66.

c.

Expert Solution
Check Mark
To determine

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,

P(zZz)=0.2052P(Zz)P(Zz)=0.2052P(Zz)[1P(Zz)]=0.20522P(Zz)1=0.2052P(Zz)=1+0.20522P(Zz)=1.20522P(Zz)=0.6026

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:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 6.2, Problem 15E , additional homework tip  3

Hence, P(Z0.26)=0.6026.

Thus, value of z is 0.26.

d.

Expert Solution
Check Mark
To determine

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 P(Zz)=0.9948.

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:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 6.2, Problem 15E , additional homework tip  4

Hence, P(Z2.56)=0.9948.

Thus, the value of z is 2.56.

e.

Expert Solution
Check Mark
To determine

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,

P(Zz)=0.69151P(Zz)=0.6915P(Zz)=10.6915P(Zz)=0.3085

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:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 6.2, Problem 15E , additional homework tip  5

Hence, P(Z0.50)=0.3085.

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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