The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $2000 and the standard deviation is $65.
What is the approximate percentage of buyers who paid between $1935 and $2065?
To find the percentage of buyers who paid between $1935 and $2065, we can use the properties of the normal distribution.
First, we need to calculate the z-scores for these two prices. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x = individual price
μ = mean price
σ = standard deviation
For $1935:
z1 = (1935 - 2000) / 65 = -1
For $2065:
z2 = (2065 - 2000) / 65 = +1
We can now use a standard normal distribution table or calculator to find the area between z1 and z2. The area under the curve represents the percentage of buyers who paid between $1935 and $2065.
Using a standard normal distribution table or calculator, we find that the area between -1 and +1 is approximately 68%.
Therefore, approximately 68% of buyers paid between $1935 and $2065 for the particular model of HD television.