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 $1870 and $2000?
To find the approximate percentage of buyers who paid between $1870 and $2000, we need to calculate the area under the normal distribution curve between these two values.
First, we need to standardize the values using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For $1870:
z1 = (1870 - 2000) / 65 = -0.2
For $2000:
z2 = (2000 - 2000) / 65 = 0
Next, we can use a table or a calculator to find the area between these two z-scores.
Using a standard normal distribution table, the z-value for -0.2 is approximately 0.4207. The z-value for 0 is 0.5.
The area between these two z-values is approximately 0.5 - 0.4207 = 0.0793.
To find the percentage, we multiply this value by 100:
0.0793 * 100 ≈ 7.93%
Approximately 7.93% of buyers paid between $1870 and $2000 for the HD television model.