A health insurance company in country A sells policies to tourists who intend to visit the US for less than 3 months. To limit its financial exposure, it requires applicants to undertake a physical examination and meet specified criteria for different tests. To simplify the problem, let us assume that only one test is done and it measures cholesterol level of the applicant. Historical records in country A indicate that cholesterol level is normally distributed with a mean of 225 milligrams per deciliter (mg/dL) and a standard deviation of 39.5 mg/dL. High cholesterol levels increase the risk of a cardiovascular incident, for which the company may need to make major insurance payouts. The premium charged is a flat $3000/person for those who qualify. For planning purposes, assume the company will get 100,000 applications in a particular year. [show your calculations for all parts] a. The current threshold T for cholesterol is set by the company at 250 mg/dL. Anyone whose test result is greater than T is denied a policy. How many applications will be denied as a result of this rule? b. If the company wants to deny policies to applicants who are in the top 10% of cholesterol values, at what value should T be set? c. An executive at the company says that they can increase revenue by increasing T from 250 to 275. Quantify the revenue increase.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A health insurance company in country A sells policies to tourists who intend to visit the US for less than 3 months. To limit its financial exposure, it requires applicants to undertake a physical examination and meet specified criteria for different tests. To simplify the problem, let us assume that only one test is done and it measures cholesterol level of the applicant. Historical records in country A indicate that cholesterol level is
a. The current threshold T for cholesterol is set by the company at 250 mg/dL. Anyone whose test result is greater than T is denied a policy. How many applications will be denied as a result of this rule?
b. If the company wants to deny policies to applicants who are in the top 10% of cholesterol values, at what value should T be set?
c. An executive at the company says that they can increase revenue by increasing T from 250 to 275. Quantify the revenue increase.
d. In less than 100 words, discuss how the company could use its internal historical data to determine the likely impact on net income (i.e. revenue – costs) of changing T from 250 to 275?
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