Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.1 and a standard deviation of 40.4. All units are in mg/100 mL. Find the two levels that separate the top 9% and the
Bottom 9%.
A) 161.5 mg/100mL and 194.7 mg/100mL
B) 107.8 mg/100mL and 248.4 mg/100mL
C) 124.0 mg/100mL and 232.2 mg/100mL
D) 165.2 mg/100mL and 191.03 mg/100mL

Question

Quizplus · Accepted Answer

Using a z-score calculator or a standard normal distribution table, we find that the z-score for the top 9% is approximately 1.34 and the z-score for the bottom 9% is approximately -1.34. We can then use the formula z = (x - μ) / σ to solve for the corresponding cholesterol levels x. 
For the top 9%: 1.34 = (x - 178.1) / 40.4, which gives x ≈ 232.2 mg/100mL.
For the bottom 9%: -1.34 = (x - 178.1) / 40.4, which gives x ≈ 124.0 mg/100mL.
Therefore, the two levels that separate the top and bottom 9% are approximately 124.0 mg/100mL and 232.2 mg/100mL. Rounding to the nearest tenth, we get the answer choice C.

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