The cholesterol levels of adult American women are approximately normal with the mean of 188 mg/dl and a standard deviation of 24 mg/dl. a company wants to test a certain medication for women falling in the highest 15% of cholesterol readings. what is the lowest cholesterol reading a women might have and still be in the test group? never done these type of problems so it would h.elp on this one so I could do others
Just go here
http://davidmlane.com/hyperstat/z_table.html
but how do use percent?
To find the lowest cholesterol reading for women that falls into the highest 15% group, we need to determine the z-score associated with this percentile and then use it to calculate the corresponding cholesterol level.
Here are the steps to solve this problem:
Step 1: Convert the desired percentile to a z-score.
The highest 15% of cholesterol readings correspond to the area to the right of this percentile in a standard normal distribution. Since the normal distribution is symmetric, we can find the z-score that corresponds to the area to the left of this percentile, which is 1 - 0.15 = 0.85.
Using a standard normal distribution table or a calculator, we can find the z-score associated with an area of 0.85. In this case, the z-score is approximately 1.036.
Step 2: Calculate the cholesterol level using the z-score.
The formula to calculate the cholesterol level is:
Cholesterol Level = Mean + (z-score * Standard Deviation)
Substituting the given values:
Mean = 188 mg/dl
Standard Deviation = 24 mg/dl
z-score = 1.036
Cholesterol Level = 188 mg/dl + (1.036 * 24 mg/dl)
Calculating the result:
Cholesterol Level = 188 mg/dl + 24.864 mg/dl
Cholesterol Level ≈ 212.864 mg/dl
Therefore, the lowest cholesterol reading a woman might have and still be in the test group is approximately 212.864 mg/dl.