Question

scores on an exam required for all medical school applicants were approximately normal with a mean of 420 and a standard deviation of 8.2.

a.) suppose an applicant had a test score of 520. what percentile corresponds with this score?

b.) suppose to be considered at a highly selective school and applicant need to score the top 10%. what score would place the applicant on top of 10%

Answer 1

Here' the answer to the question. please write back in case you've doubts.

We refer to the Z-tables to answer the questions.

Normal distribution parameters are given :

Mean = 420
Stdeve = 8.2 [please note that the stdev is 8.2, as given in the question. ]

Standardizing formula, Z = (X-Mean)/Stdev

a. For, X = 520 the Z-score is : (520-420)/8.2 = 12.2
transalating this to percentile it is : P(Z<12.2) = 1.00 or 100% percentile

b. lets say we have to score "s" to be in top 10%
So, P(X>c) = .10
Standardizing:
(c-520)/8.2 = -1.28155 [-1.28155 is the Z-equivalent to top .10 probability ]
c = -1.28155*8.2 + 520
c = 509.49 or 510

So, if applicant' score is 510 then applicant is in to 10% in the class