Question

The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rob is an engineer. The mean salary for engineers with less than 5 years’ experience is $60,000 with a standard deviation of $5,000. Rachel works in the retail industry, where the mean salary for executives with less than 5 years’ experience is $35,000 with a standard deviation of $8,000.

Compute the z values for both Rob and Rachel and comment on your findings.

Answer 1

z-value of rachel = 1.875

z-value of rob = -2

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.

Explanation:

Let's denote the salary of Rob and Rachel per year by X. So, X = $50,000

We are told that;

For Rachel's industry;

Mean salary;μ1 = $35,000

Standard deviation;σ1 = $8,000

For Rob's industry;

Mean salary;μ2 = $60,000

Standard deviation;σ2 = $5,000

Formula for z - value is;

z = (X - μ)/σ

Thus;

z-value for rob is;

z2 = (X - μ2)/σ2

z2 = (50000 - 60000)/5000

z2 = -2

z-value for rachel is;

z1 = (X - μ1)/σ1

z1 = (50000 - 35000)/8000

z1 = 1.875

z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.