A 46-year-old man comes to the office due to loose teeth and inflammation in his gums. After periodontal evaluation, the diagnosis of localized aggressive chronic periodontitis (CP) is suspected. Laboratory results, including C-reactive protein (CRP) results, are pending. Results from a recent cross-sectional study evaluating serum CRP levels in 100 subjects with aggressive CP has found that the mean CRP concentration among these subjects is 6 mg/dL ± 1 mg/dL. If the population has a normal distribution, what is the probability that this patient has a CRP ≥9 mg/dL?

Question

A 46-year-old man comes to the office due to loose teeth and inflammation in his gums.  After periodontal evaluation, the diagnosis of localized aggressive chronic periodontitis (CP) is suspected.  Laboratory results, including C-reactive protein (CRP) results, are pending.  Results from a recent cross-sectional study evaluating serum CRP levels in 100 subjects with aggressive CP has found that the mean CRP concentration among these subjects is 6 mg/dL ± 1 mg/dL.  If the population has a normal distribution, what is the probability that this patient has a CRP ≥9 mg/dL?

Quizplus · Accepted Answer

Explanation: 11ec2b69_c0f3_660e_8f63_331474c0d240_MD0005_00 A normal distribution refers to a symmetrical, bell-shaped distribution pattern with a fixed proportion of observations lying within a certain distance of the mean. 68% of all observations lie within 1 standard deviation (SD) of the mean, with half of those above and half below the mean. The remaining 32% (100% − 68% = 32%) lie outside 1 SD from the mean, with half (ie, 16%) above and half (ie, 16%) below 1 SD from the mean. Similarly, 95% of all observations lie within 2 SDs of the mean (with 5% outside 2 SDs from the mean), and 99.7% of all observations lie within 3 SDs of the mean (with 0.3% outside 3 SDs from the mean). This is commonly known as the "68-95-99.7 rule." Based on the study results, serum levels of C-reactive protein (CRP) among subjects with localized aggressive chronic periodontitis are normally distributed with a mean of 6 and a SD of 1 mg/dL. Therefore: 68% of CRP values lie within 1 SD: 6 mg/dL ± 1 mg/dL = 5-7 mg/dL, with 100% − 68% = 32% (or 0.32) lying outside 1 SD. Therefore, (32%)/2 = 16% (or 0.16) will be ≤5 mg/dL and 16% (or 0.16) will be ≥7 mg/dL (Choice E). 95% of CRP values lie within 2 SDs: 6 mg/dL ± 2 mg/dL = 4-8 mg/dL, with 100% − 95% = 5% (or 0.05) lying outside 2 SDs (Choice D). Therefore, (5%/2) = 2.5% (or 0.025) will be ≤4 mg/dL and 2.5% (or 0.025) will be ≥8 mg/dL (Choice C). 99.7% of CRP values lie within 3 SDs: 6 mg/dL ± 3 mg/dL = 3-9 mg/dL, with 100% − 99.7% = 0.3% (or 0.003) lying outside 3 SDs (Choice B). Therefore, (0.3%/2) = 0.15% (or 0.0015) will be ≤3 mg/dL and 0.15% (0.0015) will be ≥9 mg/dL. For this patient, because the cutoff point of ≥9 mg/L lies 3 SDs above the mean, the probability of CRP ≥9 mg/dL is 0.15% = 0.0015. Educational objective: In a normal distribution, 68% of all values are within 1 standard deviation (SD) from the mean; 95% of all values are within 2 SDs from the mean; and 99.7% of all values are within 3 SDs from the mean.

A 46-Year-Old Man Comes to the Office Due to Loose