Question

You plan to purchase dental insurance for your three remaining years in school. The insurance makes a​ one-time payment of $1300 in case of a major dental repair​ (such as an​ implant) or a​ one-time payment of $200 in case of a minor repair​ (such as a​ cavity). If you​ don't need dental repair over the next 3 ​ years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years as 5% a minor repair as 58% and no repair as 37%.

Why is X= payout of dental insurance a random variable?

a)The amount of the payout for​ major, minor, or no dental repair varies over the next 3 years.

b)The value of the payout depends on whether you will need​ major, minor, or no dental repair over the next 3 years.

c)The probability of needing​ major, minor, or no dental repair over the next 3 years varies.

d)The probability of needing​ major, minor, or no dental repair over the next 3 years is estimated.

Answer 1

The amount of the payout for​ major, minor, or no dental repair varies over the next 3 years with specific probabilities so this would be a random variable.

Option A is correct.