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

(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:

(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)

Therefore, the probability distribution of X is given below:

1/800 is the right answer

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.