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In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of claims on a randomly selected car of one model. The probability distribution of C is given below.
c $0 $1000 $4000 $10000
P(c) 0.6 0.05 0.13 0.22
Which of the following is the probability that the insurance company will have to pay a claim of at least $1000 for a randomly selected car of this model?
a. 0.05
b. 0.13.
c. 0.22.
d. 0.35.
e. 0.406.
f. none of above

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Answer:

0.4

None of the above

Explanation:

Given the distribution :

c ___$0 ___ $1000 ____ $4000 ___ $10000

P(c) _0.6 ____0.05 ______ 0.13 _____ 0.22

Probability of atleast $1000 :

P(x ≥ 1000) : P(x = 1000) + P(x = 4000) + P(x = 10000)

P(x ≥ 1000) = 0.05 + 0.13 + 0.22

P(x ≥ 1000) = 0.4

The probability of the insurance company having to pay the claim of a minimum of $1000 for a randomly opted car's model would be:

e). 0.406

As per the data provided,

c                             P(c)

$0                            0.6

$1000                     0.05

$4000                     0.13

$10000                    0.22

Probability of insurance company having to pay the claim of a minimum of $1000 for a randomly opted car's model(P):

[tex]P(x[/tex] [tex]\geq[/tex] [tex]1000) : P(x = 1000) + P(x = 4000) + P(x = 10000)[/tex]

[tex]P(x \geq 1000)[/tex] [tex]= 0.05 + 0.13 + 0.22[/tex]

∵ [tex]P(x \geq 1000)[/tex] [tex]= 0.406[/tex]

Thus, option e is the correct answer.

Learn more about "Probability" here:

brainly.com/question/11234923

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