Question

Diabetic patients have normally distributed cholesterol with mean 200 mg/dL and standard deviation=10 mg/dL. Sami is one of them and his cholesterol is 205. Find the percentage of patients whose cholesterol is below Sami's cholesterol

Answer 1

To determine the percentage of patients with cholesterol below 205 mg/dL, Sami's z-score is calculated as 0.5. Referring to the normal distribution, approximately 69.15% of patients would have cholesterol levels below Sami's.

Step-by-step explanation:

To find the percentage of diabetic patients whose cholesterol is below Sami's 205 mg/dL, using a normal distribution with a mean of 200 mg/dL and a standard deviation of 10 mg/dL, we first calculate Sami's z-score:

Z = (X - μ) / σ

Z = (205 - 200) / 10 = 0.5

Using a standard normal distribution table, or a calculator with normal distribution functions, we can find the probability corresponding to a z-score of 0.5. This probability indicates the proportion of patients with cholesterol levels below 205 mg/dL.

Usually, the probability associated with a z-score of 0.5 is approximately 0.6915. Therefore, approximately 69.15% of patients would have cholesterol levels below Sami's. This means that Sami's cholesterol level is higher than about 69.15% of diabetic patients.