Question

Quantiative Methods for Business : STANARDIZING

Consider that a company hiring a candidate requests a resume that includes the candidate's grade transcripts. The company receives 100 resumes and transcripts that includes the candidate's grade point average. Next, the company decides to interview the top 10% candidates, i.e., the top 10% GPA's. Questions: 1. Could a company do this? 2. If yes, what would the process be, i.e., how would it go about doing this? 3. If the mean of the population is 3.5 and the standard deviation is .1, what GPA score is necessary for the top 10%?

Answer 1

Solution :

Given that,

mean = $\mu$ = 3.5

standard deviation = $\sigma$ = 0.1

n = 100

$\mu$ _{$\bar x$} = 3.5

$\sigma$ _{$\bar x$} = $\sigma$ / $\sqrt$ n = 0.1 / $\sqrt$ 100 = 0.1 / 10 = 0.01

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

P(Z < 1.28) = 0.90

z = 1.28

$\bar x$ = z * $\sigma$ _{$\bar x$} + $\mu$ _{$\bar x$} = 1.28 * 0.01 + 3.5 = 3.5128

GPA score = 3.5128