Question

suppose that jason recently landed job offers at two companies. company a reports an average salary of $51,500 with a standard deviation of $2,150. company b reports an average salary of $46,820 with a standard deviation of $5,890. assume that salaries at each company are normally distributed.

jasons goal is to secure a position that pays $55,000 per year. what are the z - scores for jasons desired salary at company a and company b?
(round to 2 decimal places.)

company a: $z=$
company b: $z=$

at which company is jason more likely to obtain his desired salary of $55,000 per year?
company b, because the z - score for $55,000 at company b is less than the z - score for $55,000 at company a.
company a, because the z - score for $55,000 at company a is less than the z - score for $55,000 at company b.
company b, because the z - score for $55,000 at company b is greater than the z - score for $55,000 at company a.
company a, because the z - score for $55,000 at company a is greater than the z - score for $55,000 at company b.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for Company A

For Company A, $\mu = 51500$, $\sigma=2150$, and $x = 55000$. Then $z_A=\frac{55000 - 51500}{2150}=\frac{3500}{2150}\approx1.63$.

Step3: Calculate z - score for Company B

For Company B, $\mu = 46820$, $\sigma = 5890$, and $x = 55000$. Then $z_B=\frac{55000-46820}{5890}=\frac{8180}{5890}\approx1.39$.

Answer:

Company A: $z = 1.63$
Company B: $z = 1.39$
Company A, because the z - score for $55,000$ at Company A is greater than the z - score for $55,000$ at Company B.