Question

Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $19,000 and the standard deviation is $2000. Use the 68-95-99.7 Rule to find the percentage of buyers who paid more than $21,000.

Answer 1

The percentage of buyers who paid more than 21000 is 68%

Using the parameters given for our Calculation:

• mean, μ = 19000
• standard deviation, σ = 2000
• buyer who paid , x = 21000

Calculating the Zscore :

• Zscore = (x - mean) / standard deviation

Inputting our values :

Zscore = (21000 - 19000) / 2000

Zscore = 1

Using the empirical rule ;

• 1 standard deviation = 68%
• 2 standard deviations = 95%
• 3 standard deviations = 99.7%

Since, 21000 is 1 standard deviation from the mean, Then percentage of buyers who paid more than 21000 is 68%