Question

In class there was mention of Air Force jobs which required ASVAB scores to fall between a minimum and maximum score.  Assuming that scores are drawn from a Gaussian distribution with mean 50 and standard deviation 10, what proportion of recruits would qualify for a job with min=45 and max=60?

Answer 1

X = ASVAB scores

So X follows Gaussian distribution with mean 50 and standard deviation 10,

Here we want to find  proportion of recruits would qualify for a job with min=45 and max=60?

Mathematically, we want to find P( 45 < X < 60) = P(X < 60) - P(X < 45) ........( 1 )

Let's use excel:

P(X < 60) = "=NORMDIST(60,50,10,1)" = 0.8413

P(X < 45)  = "=NORMDIST(45,50,10,1)" = 0.3085

Plug these values in equation ( 1 ), we get

P( 45 < X < 60) = 0.8413 - 0.3085 = 0.5328

Look the following image: