SOLUTION: To qualify for security officers training, recruits are tested for stress tolerance. The scores are normally distributed with a mean of 70 and a standard deviation of 5. If only th

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Question 973097: To qualify for security officers training, recruits are tested for stress tolerance. The scores are normally distributed with a mean of 70 and a standard deviation of 5. If only the top 25% of recruits are selected, find the cut-off score. What is the percentile rank of that sore? ( 10 points)

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To qualify for security officers training, recruits are tested for stress tolerance. The scores are normally distributed with a mean of 70 and a standard deviation of 5. If only the top 25% of recruits are selected, find the cut-off score. What is the percentile rank of that sore?
Solution:
P(Z > 0.67) ≈ 0.25
%28x-%28mu%29%29%2F%28sigma%29 = 0.67
%28x-70%29%2F5 = 0.67
x = 0.67*5 + 70 = highlight%2873.4%29 [1 decimal place]
73.4 is the 75th percentile point.