HCI Sampling Tutorial Q10

Cholesterol molecules are transported in blood by large macromolecular assemblies (illustrated below) called lipoproteins that are really a conglomerate of molecules including apolipoproteins, phospholipids, cholesterol and cholesterol esters.

This macromolecular carrier particles make it possible to transport lipid molecules in blood, which is essentially an aqueous system.

Different classes of these lipid transport carriers can be separated (fractionated) based on their density and where they layer out when spun in a centrifuge.High-density lipoprotein cholesterol (HDL) is sometimes referred to as the ‘good cholesterol,’ because higher concentrations of HDL in blood are associated with a lower risk of coronary heart disease.In contrast, high concentrations of low-density lipoprotein cholesterol (LDL) are associated with an increased risk of coronary heart disease.The illustration above outlines how total cholesterol levels are classified in terms of risk, and how the levels of LDL and HDL fractions provide additional information regarding risk.

1. Data from the Framingham Heart Study found that subjects over age \(50\) had a mean HDL of \(54\) and a standard deviation of \(17\). Suppose a physician has \(40\) patients over age \(50\), what is the probability that the mean HDL cholesterol for this sample of \(40\) patients could be classified as low risk? What is the probability that the mean HDL cholesterol among these \(40\) patients is less than \(50\)?
2. We know from studies of adults under age \(65\) that the standard deviation is \(13\), and we will assume that the variability in LDL in adults \(65\) years of age and older is the same. We will select a sample of \(100\) participants \(65\) years of age and older, and we will use the mean of this sample as an estimate of the population mean. What is the probability that our estimate will be within \(3\) units of the population mean LDL cholesterol in the population of adults \(65\) years of age and older?