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 140 or more must be obtained. In a recent examination, it was found that the scores were normally distributed with a mean of 130 points and a standard deviation of 23 points. Determine the percentage of applicants who passed the written qualifying examination. (Round your answer to two decimal places.)

Answer 1

Here, μ = 130, σ = 23 and x = 140. We need to compute P(X >= 140). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (140 - 130)/23 = 0.43

Therefore,
P(X >= 140) = P(z <= (140 - 130)/23)
= P(z >= 0.43)
= 1 - 0.6664
= 0.3336

Hence 33.36% of applicants passed the exam