HDL also known as good cholesterol is one of the ve major gr

HDL, also known as “good cholesterol” is one of the ve major groups of lipoproteins. HDL levels greater than 60 mg/dL are benecial, and HDL levels less than 40 mg/dL are cause for concern. A random sample of 11,123 Americans had a sample mean HDL level of 47 mg/dL with a standard deviation of 13.4 mg/dL and standard error of 0.13 mg/dL. Using this sample as an estimate for population mean and standard deviation, and assuming HDL levels are normally distributed, what percentage of Americans have HDL levels that are cause for concern? Round to four decimal places.

Please show all work. Thanks

Solution

HDL, also known as “good cholesterol” is one of the ve major groups of lipoproteins.

HDL levels greater than 60 mg/dL are benecial, and HDL levels less than 40 mg/dL are cause for concern.

A random sample of 11,123 Americans had a sample mean HDL level of 47 mg/dL with a standard deviation of 13.4 mg/dL and standard error of 0.13 mg/dL.

Using this sample as an estimate for population mean and standard deviation, and assuming HDL levels are normally distributed,

Let X be a random variable that HDL level.

n = number of Americans = 11123

Xbar = 47 mg/dL

sd = 13.4 mg/dL

se = 0.13 mg/dL

what percentage of Americans have HDL levels that are cause for concern?

That is we have to calculate P(Americans have HDL levels that are cause for concern)

P(X < 40)

Now we have to find z-score for X=40,

z = (x - mean) / sd

z = (40 - 47) / 13.4 = - 0.52

That is now we have to find P(Z < - 0.52)

This we can done by using EXCEL.

syntax :

=normsdist(z)

z = -0.52

P(Z < - 0.52) = 0.3015

The percentage of Americans have HDL levels that are cause for concern is 30.15%.