Question

You plan to purchase dental insurance for your three remaining years in school. The insurance makes a​ one-time payment of ​$1200 in case of a major dental repair​ (such as an​ implant) or a​ one-time payment of ​$160 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 6​%, a minor repair as 59​% and no repair as 35​%. Complete parts a through c.

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

A. The amount of the payout for major, mincr, or no dental repair varies over the next 3 years.
B. The probability of needing major, minor or no dental repair over the next 3 years is estimated.
C. The probability of needing major, minor, or no dental repair over the next 3 years varies.
D. The value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years.

b. Is X discrete or continuous? What are its possible values?
c. Give the probability distribution of X

Answer 1

Answer:

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

(b)Discrete

(c) See below

Step-by-step explanation:

• For a major dental repair, the insurance company pays $1200
• For a minor dental repair, the insurance company pays $160
• For no dental repair, the insurance company pays $0

(a) X= payout of dental insurance a random variable

The payout of dental insurance, X is a random variable because the value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years. The correct option is D.

(b) X is a discrete variable. This is because its values are whole numbers.

The possible values are $1200, $160 and $0.

(c)

• The probability of requiring a major dental repair (with payout of $1200) is 6%.

• The probability of requiring a minor dental repair (with payout of $160) is 59%.

• The probability of requiring no dental repair (with payout of $0) is 35%.

Therefore, the probability distribution of X is given below:

$\left|\begin{array}{c|c|c|c}--------------&---&---&---\\X (Payout of dental insurance)&\ 1200&\ 160&\ 0\\--------------&---&---&---\\P(X)&0.06&0.59&0.35\\--------------&---&---&---\end{array}\right|$