Answer:
98th percentile.
Explanation:
We have been given that an average new car costs $23,000, with a standard deviation of $3,500.
Since the price of cars are normally distributed, so we will find z-score for a car sold for $30,000 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Random sample score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Substitute the given values:
[tex]z=\frac{\$30,000-\$23,000}{\$3,500}[/tex]
[tex]z=\frac{\$7,000}{\$3,500}[/tex]
[tex]z=2[/tex]
Now, we will use normal distribution table to find what percent of data is below a z-score of 2.
[tex]p(z<2)=0.97725 [/tex]
Convert 0.97725 to percentage:
[tex].97725\times 100\%=97.725\%\approx 97.73\%[/tex]
Therefore, the car that is sold for $30,000 has a percentile rank of 98.
