Question

you are applying for a job at two companies. company a offers starting salaries with $mu = 28000$ and $sigma = 2000$. company b offers starting salaries with $mu = 28000$ and $sigma = 5000$. from which company are you more likely to get an offer of $32000$ or more?
choose the correct answer below
a. company a, because data values that lie more than two standard - deviations from the mean are considered unusual
b. company b, because data values that lie within one standard deviation from the mean are not considered unusual
c. no difference, because data values that lie more than three standard deviations from the mean are considered very unusual

Explanation:

Step1: Calculate z - score for Company A

The z - score formula is $z=\frac{x-\mu}{\sigma}$. For Company A, $\mu = 28000$, $\sigma=2000$, and $x = 32000$. So $z_A=\frac{32000 - 28000}{2000}=\frac{4000}{2000}=2$.

Step2: Calculate z - score for Company B

For Company B, $\mu = 28000$, $\sigma = 5000$, and $x = 32000$. So $z_B=\frac{32000 - 28000}{5000}=\frac{4000}{5000}=0.8$.

Step3: Analyze the probabilities

A higher z - score means the value is further from the mean. A lower z - score implies a higher probability of getting a value at or above that point. Since $z_B

Answer:

B. Company B, because data values that lie within one standard deviation from the mean are not considered unusual