On an auto mechanic aptitude test, the mean score is 271 points and the standard

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

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