Question

carlos and devon both accepted new jobs at different companies. carloss starting salary is $30,000 and devons starting salary is $30,000. they are curious to know who has a better starting salary when compared to the salary distributions of their new employers.
a website that collects salary information from a sample of employees for a number of major employers reports that carloss company offers a mean salary of $47,000 with a standard deviation of $7,000. devons company offers a mean salary of $40,000 with a standard deviation of $6,000.
find the z - scores corresponding to each of their starting salaries. round to two decimal places, if necessary.
provide your answer below.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value (in this case, the starting salary), $\mu$ is the mean of the distribution, and $\sigma$ is the standard deviation of the distribution.

Step2: Calculate Carlos's z - score

For Carlos: $x = 30000$, $\mu=47000$, $\sigma = 7000$.
Substitute into the formula: $z_{Carlos}=\frac{30000 - 47000}{7000}=\frac{- 17000}{7000}\approx - 2.43$

Step3: Calculate Devon's z - score

For Devon: $x = 30000$, $\mu = 40000$, $\sigma=6000$.
Substitute into the formula: $z_{Devon}=\frac{30000 - 40000}{6000}=\frac{-10000}{6000}\approx - 1.67$

Answer:

Carlos's z - score: $\boldsymbol{-2.43}$; Devon's z - score: $\boldsymbol{-1.67}$