Respuesta :
Answer:
The z-score for Jack's desired salary at company A is 1.61.
The z-score for Jack's desired salary at company B is 1.38.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
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 problem, we have that:
Company A:
Company A reports an average salary of $51,500 with a standard deviation of $2,175. This means that [tex]\mu = 51500, \sigma = 2175[/tex]
Jason's goal is to secure a position that pays $55,000 per year. What isthe z ‑score for Jason's desired salary at Company A?
This is Z when X = 55000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55000 - 51500}{2175}[/tex]
[tex]Z = 1.61[/tex]
The z-score for Jack's desired salary at company A is 1.61.
Company B:
Company B reports an average salary of $46,820 with a standard deviation of $5,920. This means that [tex]\mu = 46820, \sigma = 5920[/tex].
Jason's goal is to secure a position that pays $55,000 per year. What isthe z ‑score for Jason's desired salary at Company B?
This is Z when X = 55000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55000 - 46820}{5920}[/tex]
[tex]Z = 1.38[/tex]
The z-score for Jack's desired salary at company B is 1.38.
