Question

The cholesterol levels of an adult can be described by a normal model with the mean of 195 mg/dL and a standard deviation of 28 What percent of adults do you expect to have cholesterol levels over 200 round 2 decimal places

Answer 1

Using the normal distribution model with a mean of 195 mg/dL and a standard deviation of 28 mg/dL, approximately 42.86% of adults are expected to have cholesterol levels over 200 mg/dL.

Step-by-step explanation:

To calculate the percentage of adults expected to have cholesterol levels over 200 mg/dL, we will use the normal distribution model provided. With a mean of 195 mg/dL and a standard deviation of 28 mg/dL, we first need to find the Z-score for a level of 200 mg/dL:

Z = (X - μ) / σ

Z = (200 - 195) / 28 ≈ 0.18

Next, we consult a standard normal distribution table or use a calculator with normal distribution functions to find the tail probability associated with a Z-score of 0.18. This gives us the percentage of people with cholesterol levels above 200 mg/dL. For a Z-score of 0.18, the area to the left is approximately 0.5714, which means the area to the right (over 200 mg/dL) is 1 - 0.5714 = 0.4286 or 42.86%. Therefore, we expect 42.86% of adults to have cholesterol levels over 200 mg/dL.

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