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.

1. Compute the z values for both Rob and Rachel. (Round your answers to 2 decimal places. Negative amount should be indicated by a minus sign.)

Rob:

Rachel:

Comment on your findings.

Adjusting for their industries, Rob is well ________ (Above/Below) average and Rachel well _________ (above/below)

Answer 1

Rob:

Here, μ = 60000, σ = 5000 and x = 50000. We need to compute P(X <= 50000). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (50000 - 60000)/5000 = -2

Rachel:

Here, μ = 35000, σ = 8000 and x = 50000. We need to compute P(X <= 50000). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (50000 - 35000)/8000 = 1.88

Adjusting for their industries, Rob is well Below average and Rachel well above average