Question

II. 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? b. What is a Z score for a car with a price of $30,000?

Answer 1

Answer:

a) Z = 2.86

b) Z = 2

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 23000, \sigma = 3500$

a. What is a Z score for a car with a price of $33,000?

This is Z when X = 33000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33000 - 23000}{3500}$

$Z = 2.86$

b. What is a Z score for a car with a price of $30,000?

This is Z when X = 30000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30000 - 23000}{3500}$

$Z = 2$