Respuesta :
Answer:
a) Z = 2.86
b) Z = 2
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 23000, \sigma = 3500[/tex]
a. What is a Z score for a car with a price of $33,000?
This is Z when X = 33000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33000 - 23000}{3500}[/tex]
[tex]Z = 2.86[/tex]
b. What is a Z score for a car with a price of $30,000?
This is Z when X = 30000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30000 - 23000}{3500}[/tex]
[tex]Z = 2[/tex]
