An intern in the endocrinology department is asked to complete a chart review of cholesterol levels of all patients hospitalized with diabetes mellitus-related cardiovascular complications in the past 6 months. The intern's preliminary data analysis reveals that there were 400 such patients, and that serum cholesterol levels were normally distributed among the patients with a mean of 220 mg/dL and a standard deviation of 10 mg/dL. Based on these results, how many patients in this study would be expected to have serum cholesterol 240 mg/dL?

Question

An intern in the endocrinology department is asked to complete a chart review of cholesterol levels of all patients hospitalized with diabetes mellitus-related cardiovascular complications in the past 6 months.  The intern's preliminary data analysis reveals that there were 400 such patients, and that serum cholesterol levels were normally distributed among the patients with a mean of 220 mg/dL and a standard deviation of 10 mg/dL.  Based on these results, how many patients in this study would be expected to have serum cholesterol >240 mg/dL?

Quizplus · Accepted Answer

11ec160b_3707_ebba_9249_9bee52146d6f_MD0001_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. This distance is called the standard deviation (SD) and is a measure of the degree of dispersion from the mean. When the SD is small, the observations tend to have minimal variation and are tightly clustered around the mean. In contrast, a large SD implies that the observations are spread over a large range. According to the properties of normal distribution, 68% of all observations lie within 1 SD of the mean, with half of those above and half of those below the mean. The remaining 32% of observations lie outside 1 SD from the mean, with half of those remaining observations above and the other half below 1 SD from the mean. In addition, 95% of all observations lie within 2 SDs of the mean, and 99.7% of all observations lie within 3 SDs from the mean. This is commonly known as the "68-95-99.7 rule." Based on the above example: Because the cutoff point of >240 mg/dL is 2 SDs from the mean, it follows that 2.5% of the observations must lie below 200 mg/dL and 2.5% above 240 mg/dL. Therefore, of 400 patients included in the analysis, 10 patients (ie, 2.5%) would have a cholesterol level >240 mg/dL. (Choice A) No more than 1-2 patients (0.25%-0.5% of the study population) would be expected to have cholesterol levels that lie 3 SDs above or below the mean (ie, <190 mg/dL or >250 mg/dL). (Choice C) 20 patients (5% of the study population) would be expected to have cholesterol levels that lie outside 2 SDs from the mean. Only half of these observations would lie above 2 SDs (ie, >240 mg/dL) from the mean. (Choice D) 64 patients (16% of the study population) would be expected to have cholesterol levels that lie 1 SD above the mean (ie, >230 mg/dL). (Choice E) 128 patients (32% of the study population) would be expected to have cholesterol levels that lie 1 SD above or below the mean (ie, >230 mg/dL or <210 mg/dL). Educational objective: In a normal (bell-shaped) distribution: 68% of all values are within 1 standard deviation from the mean; 95% of all values are within 2 standard deviations from the mean; 99.7% of all values are within 3 standard deviations from the mean.

An Intern in the Endocrinology Department Is Asked to Complete