According to her doctor, Mrs. Scott's cholesterol level is higher than only 15% of the females aged 50 and over.

Question

According to her doctor, Mrs. Scott's cholesterol level is higher than only 15% of the females aged 50 and over. The cholesterol levels among females aged 50 and over are approximately normally distributed with a mean of 225 mg/dL and a standard deviation of 30 mg/dL. What is Mrs. Scott's cholesterol level? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. 

Answer 1

Applying z-score formula for the standard normal distribution:

z = (X - μ) / σ

where:

X = Mrs. Scott's cholesterol level

μ = mean of cholesterol levels for females aged 50 and over = 225 mg/dL

σ = standard deviation of cholesterol levels for females aged 50 and over = 30 mg/dL

We also know that her cholesterol level is higher than only 15% of the females aged 50 and over. This means her z-score corresponds to the 15th percentile (z = -1.0364 approximately).

Now, we can rearrange the z-score formula to solve for X:

X = μ + z * σ

X = 225 + (-1.0364) * 30

X = 225 - 31.092

X ≈ 193.908

Mrs. Scott's cholesterol level is approximately 193.9 mg/dL.