Question

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. At what percentile rank is a car that sold for $30,000?

Answer 1

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.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Random sample score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$.

Substitute the given values:

$z=\frac{\ 30,000-\ 23,000}{\ 3,500}$

$z=\frac{\ 7,000}{\ 3,500}$

$z=2$

Now, we will use normal distribution table to find what percent of data is below a z-score of 2.

$p(z$

Convert 0.97725 to percentage:

$.97725\times 100\%=97.725\%\approx 97.73\%$

Therefore, the car that is sold for $30,000 has a percentile rank of 98.