Hi all I am having problem with this: An educational testing corporation has des

Question

Hi all I am having problem with this:
An educational testing corporation has designed a standard test ofmechanical aptitude. Scores on this test are normally distributedwith a men of 75 and a standard deviation of 15.

a) If a subject is randomly selected andtested, find the probability that his score will be between 75 and100
b) If a subject is randomly selected and tested, find theprobability that his score will be between 70 and 90
c) If a subject is randomly selected and tested, find theprobability that his score will be between 60 and 70

Please show all work and answers, Thank You willgive a Lifesaver.

Explanation / Answer

We want to find the z-score for these test scores and then use az-table to find the p-values. z = (actual score - mean) / stdev a) z(75) = (75 - 75) / 15 = 0 --> p=.5 z(100) = (100 - 75) / 15 = 25 / 15 = 1.667 --> p = .9525 Thus, the probability of being between 75 and 100 is .9525 - .5 =.4525. b) z(70) = (70 - 75) / 15 = -.33 --> p = .3707 z(90) = (90 - 75) / 15 = 1 --> p = .8413 .8413 - .3707 = .4706 c) z(60) = (60 - 75) / 15 = -1 --> p = .1587 z(70) = (70 - 75) / 15 = -.33 --> p = .3707 .3707 - .1587 = .212

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