Answered: Let X be the total medical expenses (in… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 10E

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Let X be the total medical expenses (in 1000s of dollars) incurred by a particular individual during a given year. Although X is a discrete random variable, suppose its distribution is quite well approximated by a continuous distribution with pdf f(x) = k(1 + 2².5)¯
x ≥ 0.
(a) What is the value of k?
1.2
(b) Graph the pdf of X.
f(x)
f(x)
f(x)
f(x)
1.0
0.8
0.6
0.4
0.2
2
4
6
8
X
4
2
2
4
6
6
6
2
4
8
O
(c) What is the expected value of total medical expenses? (Round your answer to the nearest cent.)
$ 6.25
x
What is the standard deviation of total medical expenses? (Round your answer to the nearest cent.)
$ 6.25
x
(d) This individual is covered by an insurance plan that entails a $500 deductible provision (so the first $500 worth of expenses are paid by the individual). Then the plan will pay 80% of any additional expenses exceeding $500, and the maximum payment by the
individual (including the deductible amount) is $2500. Let Y denote the amount of this individual's medical expenses paid by the insurance company. What is the expected value of Y? [Hint: First figure out what value of X corresponds to the maximum out-of-pocket
expense of $2500. Then write an expression for Y as a function of X (which involves several different pieces) and calculate the expected value of this function.] (Round your answer to the nearest cent.)
$
1.0
0.8
0.6
0.4
0.2
8
X
1.0
0.8
0.6
0.4
0.2
XO
1.0
0.8
0.6
0.4
0.2

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