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Dental InsuranceHow much money will a Preventative Exam 100% patient pay out of Minor Restorative 80% pocket; including Major Restorative 5096 deductible, for a maj...

Question

Dental InsuranceHow much money will a Preventative Exam 100% patient pay out of Minor Restorative 80% pocket; including Major Restorative 5096 deductible, for a major Deductible $50,00 procedure that costs Maximum Benefit 51,500.00 $6002 Monthly Premium $30,00S480S530$300D. $350

Dental Insurance How much money will a Preventative Exam 100% patient pay out of Minor Restorative 80% pocket; including Major Restorative 5096 deductible, for a major Deductible $50,00 procedure that costs Maximum Benefit 51,500.00 $6002 Monthly Premium $30,00 S480 S530 $300 D. $350



Answers

Dental Insurance An insurance policy reimburses dental expense, $X,$ up to a maximum benefit of $250 .$ The probability density function for $X$ is
$$f(x)=\left\{\begin{array}{ll}{c e^{-0.004 x}} & {\text { for } x \geq 0} \\ {0} & {\text { otherwise,}}\end{array}\right.$$
where $c$ is a constant. Calculate the median benefit for this policy. Choose one of the following. (Hint: As long as the expenses are less than $250,$ the expenses and the benefit are equal.) Source: Society of Actuaries.
$\begin{array}{lll}{\text { (a) } 161} & {\text { (b) } 165}\end{array}$
$\begin{array}{llll}{\text { (c) } 173} & {\text { (d) } 182} & {\text { (e) } 250}\end{array}$

Problem. We're told that Kerry had to have five fillings done and each filling is gonna cost you $80. So the dental insurance is going to make you pay 20% as a co pay. So we're going to actually calculate the cost of the copay in two different methods. So in part a what they want us to do is multiply 0.20x80. Which is going to allow us to find their copay for each filling. And then we're gonna multiply that number by five to figure out the total copay because remember? Shit five fillings. Okay well let's start by multiplying 0.20 x 80. Well if I go off to the side 80 and then 0.20 that's really the same as .2. Well two times 0 is zero two times 8 is 16. But don't forget we have to move our decimal .1 place to the left which would mean to be 16.0 or simply 16. So we have 16 here. But again now we need to multiply this by five for the five fillings. So we're gonna do five times 16 which is equal to 80, Which means her total copay would have been $80. All right. So now let's go to part B. In part B. They want us to multiply five times 0.20 times 80. Okay well according to the order of operations we need to multiplying water from left to right. So first we multiply five by .20. So really if we have five times 50.22 times five is 10. But don't forget we have to move our decimal place one place to the left so at 1.0 or just one. So that leaves us with one times 80 and one times 80 is 80. So again, no that we still get the $80. Okay, so now in part C they want to know which of the properties of real numbers. Says that your answers to part A. Where you multiply five times the quantity of 0.20 times zero. Or sorry, times 80 Is the same as when we multiplied five times 0.20 times 80. Well, no this the order of the numbers didn't change. Does the order in which we multiply them change. This is referred to as the associative property. So we used the associative property to multiply these two values in different ways. Yeah.

Okay, in this problem, we know that Kerry has to have three has to have five feelings, and each filling cost $80 she has to pay 20% of it. So for each feeling she has to pay 0.2 times 80 and that is $16 then she has five feelings, so she has to pay five times 16 and that's $80 so altogether she pays $80 so that's one way to figure it out. Another way to figure it out is to do it all at once. Five feelings times 20% of 80. So if you want to do it this way, you don't have to multiply in the same order that we did in part A. You could multiply the 1st 2 numbers together first, and they happen to be a multiplicity of in verses. They multiply to give us one. So we have one times 80 which is 80. So what property did we use to do part B? Well, the property that says When you're multiplying three things, you can either multiply the 1st 2 together first or the last two together first is known as the associative property of multiplication

And this problem, we're going to determine how much an insurance company can expect to make on a policy. Now in this problem, the insurance company charges $800 a year for car insurance. And the company will pay $1,000 for a minor accident and $5,000 for a major incident. Now the probability of a motorist having a minor accident is 0.2. While the probability for having a major accident is 0.0 fight. We need to determine how much the insurance company can expect to make on a policy. Now, first of all, let us determine the expected value of how much the uh insurance company has to pay. So if X. Represents the random variable which represents the amount that the insurance company has to pay and this will be equals two submission X. Times P. X. Where X. Is the payoff and P. X. Is the probability of that respective payoff. Now, first of all, the company will pay $1,000 for a minor accident. So the first playoff is $1,000. And the probability that they will have to pay that $1,000 is equal to the probability of the motorist having a minor accident. Which is given to be 0.2. So this was a week, zero Next. Because of the submission, we add the next pay off and the probability of their pay off. So the next payoff will be $5,000 For a major accident. And with that we multiply the probability of getting that $5,000 which will happen in case of a major accident. And the probability of a major accident. 0.05. So the probability in this case will be 0.05. So 1000 Time 0.2 is equals to 205,000 times 0.05 is 250. So that means that the expected amount that the company will be will be $450. Now, we need to find out how much the insurance company can expect to make on the policy. So the insurance company charges $800 a year And they are expected to pay $450. So their profit will be $800 -4 $50 and 800 -450 Is equal to 350. So the amount of the insurance company can expect to make is $350. So in this case the correct option will be option b. The insurance company can expect to make $350 on a policy.

Okay, so let's see if these guys were gonna qualify for the IRS to cover any of that deductible or any of their medical expenses. And so the medical expenses insurance is covering 60% meaning that they're gonna pay 40% because 60 plus 40% is 100%. And so, if I multiply this by 40% I'm going to see how much they paid. And so let's do that. And it turns out that they paid 8300 and I just lost that number. It was on my screen. Bear with me for five seconds, and it's gonna be $8320. Now, there, address it. Gross income is this. And if we multiply it by 7.5% as a decimal, which is 0.75 we're going to see if the amount they paid exceeds a 7.5% that the irises considering needs to be already paid. So 101 598 Feel free to check this on your calculator. Time 0.75 ends up being $7619 in 85 cents. So yes, they have paid more than that. 7.5% in the IRS basically says this you have to pay this amount, and then on top of that, we will give you some relief. And so if you take this amount and subtract this here, we'll see how much money that are. How much the RS will provide ends up being $700.15 that the IRS can kind of cover, saying that you paid a whole lot in medical expenses more than 7.5% of your adjusted gross income. We will give you this. Who didn't mean to write this much of a basically buffer to help out with those payments?


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