Question

too much cholesterol in the blood increases the risk of heart disease. the cholesterol levels of young women aged 20 to 34 years vary approximately normally, with a mean of 200 milligrams per deciliter (mg/dl) and a standard deviation of 39 mg/dl. approximately what minimum value of the cholesterol level of young women in this age group will be placed in the top 10%?
a. 150.01
b.234.98
c. 200
d. 249.98

Explanation:

Step1: Find the z - score for the top 10%

The top 10% corresponds to an area of 0.9 to the left in the standard normal distribution. Looking up the z - score in the standard normal table (z - table), the z - score \(z\) such that \(P(Z<z)=0.9\) is approximately \(z = 1.28\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value we want to find, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. We know that \(\mu = 200\), \(\sigma=39\), and \(z = 1.28\). Rearranging the formula for \(x\) gives \(x=\mu+z\sigma\).

Step3: Calculate the value of \(x\)

Substitute the values into the formula: \(x = 200+1.28\times39\). First, calculate \(1.28\times39 = 1.28\times(40 - 1)=1.28\times40-1.28\times1=51.2 - 1.28 = 49.92\). Then \(x=200 + 49.92=249.92\approx249.98\).

Answer:

d. 249.98