Personnel tests are designed to test a job applicant\'s cognitive and/or physica

Question

Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 75 and standard deviation 7.5 .

a. A particular employer requires job candidates to score at least 79 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 79?

b. The testing service reported to a particular employer that one of its job candidate's scores fell at the 90th percentile of the distribution (i.e., approximately 90% of the scores were lower than the candidate's, and only 10% were higher). What was the candidate's score?.

a. Approximately _______% of the test scores during the past year exceeded 79 . (Round to one decimal place as needed.)

b. The candidate's score was _____. (Round to the nearest whole number as needed.)

Explanation / Answer

Mean ( u ) =75
Standard Deviation ( sd )=7.5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X > 79) = (79-75)/7.5
= 4/7.5 = 0.5333
= P ( Z >0.533) From Standard Normal Table
= 0.2969                  
b.
P ( Z > x ) = 0.1
Value of z to the cumulative probability of 0.1 from normal table is 1.2816
P( x-u/ (s.d) > x - 75/7.5) = 0.1
That is, ( x - 75/7.5) = 1.2816
--> x = 1.2816 * 7.5+75 = 84.6116 ~ 84.612

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