The 2011 gross sales of all firms in a large city has a mean of $2.5 million and a standard deviation of $0.6 million. Using Chebyshev's theorem, find at least what percentage of firms in this city had 2011 gross sales of $1.2 to $3.8 million:
The 2011 gross sales of all firms in a large city has a mean of $2.5 million and a standard deviation of $0.6 million. Using Chebyshev's theorem, find at least what percentage of firms in this city had 2011 gross sales of $1.2 to $3.8 million:
You are going to apply the Z-score for Normal Distribution and the Area of the Curve for this problem:
1. Sample Mean = 2.5
2. Standard Deviation = .6
3. X = 1.2 (X = data point)
4. X = 3.8
1st Step is to find the Z-score associated to X = 1.2
z= X - μ
σ
z= 1.2 - 2.5
.6
z = -1.3
.6
Z = -2.16
Now you need to find the Z-score associated to X = 3.8
z= X - μ
σ
z= 3.8 - 2.5
.6
z= 1.3
.6
Z = +2.16
You need to find the area of the curve that covers Z = -2.16 to Z = +2.16
Go to your Normal Distribution Table in this room
Break up 2.16 into 2.1 on the vertical and .06 on the vertical........What is at the intersection? The area of the Curve from Z = 0 to Z = +2.16 is .4846 or 48.46% AND the Area of the Curve from Z = 0 to z = -2.16 is .4846 or 48.46%
Double that and you have 96.92%
Which means that 96.92% of firms have gross sales between 1.2 to 3.8 Million
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)