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 74 and standard deviation 7.7. 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?

Answer 1

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 74 and standard deviation 7.7.

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​?

Z value for 79, z =(79-74)/7.7 = 0.65

P( x >79) = P( z > 0.65) =0.2578

The required percentage = 25.78%

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?

Z value for top 10% is 1.282

X= mean+z*sd = 74+1.282*7.7 = 83.8714

candidate's score was 83.87