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

The payout of dental insurance, X, is a random variable because its value depends on uncertain events. X is discrete with possible values of $0, $160, and $1200. The probability distribution is 35% for $0, 59% for $160, and 6% for $1200.

Step-by-step explanation:

a. X = payout of dental insurance is a random variable because D. The value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years. This is because the final payout is contingent on the occurrence of an event that is not certain, and will therefore vary.

b. X is a discrete random variable because it can take on a finite number of possible values, which, in this case, are $0 (for no repair), $160 (for minor repair), and $1200 (for major repair).

c. The probability distribution of X is as follows:

• 
  
• Value = $0, Probability = 35%
• 
  
• Value = $160, Probability = 59%
• 
  
• Value = $1200, Probability = 6%

Answer 2

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