To be eligible for further consideration, applicants for certain Civil Service positions must first pass a written qualifying examination on which a score of 70 or more must be obtained. In a recent examination it was found that the scores were normally distributed with a mean of 67 points and a standard deviation of 6 points. Determine the percentage of applicants who passed the written qualifying examination.
A) 18.79% applicants passed the written qualifying examination.
B) 19.52% applicants passed the written qualifying examination.
C) 24.74% applicants passed the written qualifying examination.
D) 30.85% applicants passed the written qualifying examination.

Question

To be eligible for further consideration, applicants for certain Civil Service positions must first pass a written qualifying examination on which a score of 70 or more must be obtained. In a recent examination it was found that the scores were normally distributed with a mean of 67 points and a standard deviation of 6 points. Determine the percentage of applicants who passed the written qualifying examination. ​
A) 18.79% applicants passed the written qualifying examination.
B) 19.52% applicants passed the written qualifying examination.
C) 24.74% applicants passed the written qualifying examination.
D) 30.85% applicants passed the written qualifying examination.

Quizplus · Accepted Answer

To find the percentage of applicants who passed the written qualifying examination, we need to find the area under the normal distribution curve to the right of the score of 70 (the passing score). We can do this by standardizing the score using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean (67), and σ is the standard deviation (6).

z = (70 - 67) / 6 = 0.5

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 0.5 is 0.3085 or 30.85%.

Therefore, the percentage of applicants who passed the written qualifying examination is 30.85%. The best choice is D.

To Be Eligible for Further Consideration, Applicants for Certain Civil