![Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337115186/9781337115186_largeCoverImage.gif)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
- Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include: Mileage (mpg) Number of Cylinders (cyl) Displacement (disp) Horsepower (hp) Research: Google to understand these variables. Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp Mean Median First Quartile (Q1) Second Quartile (Q2) Third Quartile (Q3) Fourth Quartile (Q4) 10th Percentile 70th Percentile Skewness Kurtosis Document Your Results: In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command” In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…arrow_forward2 (VaR and ES) Suppose X1 are independent. Prove that ~ Unif[-0.5, 0.5] and X2 VaRa (X1X2) < VaRa(X1) + VaRa (X2). ~ Unif[-0.5, 0.5]arrow_forward8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.arrow_forward
- 9 (Portfolio allocation) Suppose R₁ and R2 are returns of 2 assets and with expected return and variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find −∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest risk.arrow_forward7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forward
- Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forwardSolve for X. Explain each step. 2^2x • 2^-4=8arrow_forwardOne hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
![Text book image](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)