Midterm_II_Practice_Problems_V1

Midterm_II_Practice_Problems_V1 - STA 100: Midterm II...

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Unformatted text preview: STA 100: Midterm II Practice Questions For all questions you must show your working. This enables us to understand your thought process, give partial credit and prevent crude cheating. Notes About These Practice Questions: These practice questions are not a practice midterm! i.e., you would not be expected to complete all of these questions in the the time given for the midterm. Solutions to these questions will be posted after you have had sufficient time to practice them. 1. HDL Cholestrol, otherwise known as Good Cholestrol, has received much attention in re- cent years. Higher levels of HDL are considered to help reduce the risk of heart disease. HDL Cholestrol levels are measured in miligrams per deciliter of blood (mg/dl). There are variations in HDL levels between men and women. HDL levels in adult men in the general population are normally distributed with mean 52 mg/dl, and standard deviation 8 mg/dl. For women, HDL levels are normally distributed with mean 50 mg/dl and standard deviation 6 mg/dl. HDL levels for men and women are assumed to be independent. (Information from the American Heart Association). (a) Among adult males, an HDL level below 40 mg/dl provides an increased risk of heart disease. What is the proportion of men in the general population will be at increased risk of heart disease? (b) Among adult females, an HDL level below 50 mg/dl provides an increased risk of heart disease. What is the proportion of women in the general population will be at increased risk of heart disease? (c) Higher HDL levels are considered to be preventive of heart disease. An HDL level of above 60 mg/dl, for both males and females, reduces your risk of heart disease. Among the general population, are there a higher proportion of men or women that have reduced risk of heart disease? Show your working. (d) You have two friends, Bob and Jane. What is the probability that Bob has a higher level of HDL cholestrol than Jane? 2. The last decade has seen a large increase in the number of biotechnology companies. As a venture captialist with an interest in the industry, you decide to invest some money in some biotech startups. The log rate of return on your investment after 5 years, for a randomly chosen biotech startup is normally distributed with mean 0 . 02 and standard deviation 0 . 10 i.e., Y N (0 . 02 , . 1 2 ). (Note: The log rate of return is defined as Y = log( X 5 yr /X yr ) where X 5 yr is the value of your investment after 5 years, and X yr is the value of the initial investment. The important thing to note is that if Y is bigger than zero then you made some money, if Y is less than zero then you lost money.) (a) If you randomly pick a startup and invest in it, what is...
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Midterm_II_Practice_Problems_V1 - STA 100: Midterm II...

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