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
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
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