Experts consider high serum cholesterol levels to be associated with an increased incidence of coronary heart disease .suppose that the logarithm of cholesterol levels for males in a given age bracket are normally distributed with mean of 2.35 and a standard deviation of 12 .
a- what percentage of the males in this age bracket could be expected to have a serum cholesterol level greater than 250 mg/ml , the upper limit of the clinical normal range ?
To answer this question, we'll use the normal distribution and the given mean and standard deviation.
Step 1: Convert the cholesterol range to a z-score.
The z-score formula is: z = (x - μ) / σ
Where:
- x is the value we want to convert to a z-score (250 mg/ml in this case).
- μ is the mean of the distribution (2.35).
- σ is the standard deviation of the distribution (12).
For our case:
z = (250 - 2.35) / 12
Step 2: Calculate the percentage using the z-score.
We can refer to the Z-table or use a calculator to find the percentage corresponding to our z-score. Let's assume the percentage is P%.
Step 3: Interpret the result.
The percentage represents the proportion of males in this age bracket who have a serum cholesterol level greater than 250 mg/ml.
Therefore, the answer to the question is P% of the males in this age bracket could be expected to have a serum cholesterol level greater than 250 mg/ml.