On an auto mechanic aptitude test, the mean score is 271 points and the standard
ID: 3149362 • Letter: O
Question
On an auto mechanic aptitude test, the mean score is 271 points and the standard deviation is 40 points.
(a) If a student has a standardized score of 1.9, how many points is that? (Round your answer to one decimal place.)
__________ points
(b) If a student has a standardized score of 0.25, how many points is that? (Round your answer to one decimal place.)
__________ points
(c) Assuming the scores follow a normal distribution, what is the probability that a student will get between 200 and 340 points? (Round your answer to four decimal places.)
Explanation / Answer
Formula for z score is x-mean/sd
a. Here z=1.9=x-mean/sd=x-271/40
=>40*1.9=x-271
=>76+271=x
=>x=347
b. z=-0.25=x-271/40
=>40*-0.25=x-271
=>x=261
c. Here we need to find P(200<x<340)
=>P(200-271/40<z<340-271/40)
=>P(-1.775<z<1.725)
=>P(z<1.725)-P(z<=-1.775)
=>0.9577-0.0379=0.9198