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: