2. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed.
a. What is a Z score for a car with a price of $ 33,000?
Z = (33,000-23,000)/3500 = +2.86
To calculate the Z-score for a car with a price of $33,000, we need to use the formula:
Z = (X - μ) / σ
Where:
- X is the value we want to calculate the Z-score for, which in this case is $33,000.
- μ is the mean (average) of the distribution, which is $23,000.
- σ is the standard deviation of the distribution, which is $3,500.
Now, let's plug in the values into the formula:
Z = (33,000 - 23,000) / 3,500
Simplifying the equation:
Z = 10,000 / 3,500
Z ≈ 2.86
So, the Z-score for a car with a price of $33,000 is approximately 2.86.