Question

# DATA: Probability Payment 0.75 0 0.12 1000 0.08 5000 0.04 7000 0.01 10000 Questions refer to...

DATA:

 Probability Payment 0.75 0 0.12 1000 0.08 5000 0.04 7000 0.01 10000
1. Questions refer to the following problem.

The data shows the probability distribution of damage claims (\$) paid out by an insurance company last year on their collision insurance policy:

What is the average amount that the insurance can expect to pay in insurance claims?

 A. \$840 B. \$900 C. \$1,060 D. \$760

QUESTION 22

1. What is the standard deviation of the amount that the insurance can expect to pay in insurance claims?

 A. \$2060 approximately B. \$2072 approximately C. \$2066 approximately D. \$2054 approximately

QUESTION 23

1. What is the probability that the insurance company has to pay more than \$5,000 in insurance claims?

 A. 1% B. 5% C. 3% D. 4%

QUESTION 24

1. If the insurance company has already paid a claim, the probability that the claim was at least \$7,000 is:

 A. 20% B. 45% C. 25% D. 35%

QUESTION 25

1. The insurance company expects that all claims will double. What will this do the average and variance of claims paid?

 A. The mean will be unchanged, the variance will double B. The mean will double, the variance will be unchanged C. The mean will increase four times, the variance will double D. The mean will double, the variance will increase four times

 Payment (x) P(x) x* P(x) x square x 2* P(x) 0 0.75 0 0 0 1000 0.12 120 1000000 120000 5000 0.08 400 25000000 2000000 7000 0.04 280 49000000 1960000 10000 0.01 100 100000000 1000000 Total 1.00 900 175000000 5080000

(21) Expected value = x. P(x) = 1000* 0.12 + 5000* 0.08 + 7000* 0.04 + 10000* 0.01 = 900

Average amount = \$900

(22) Standard deviation

Standard deviation = \$2066

(23) P(x > 5000) = 0.04 + 0.01 = 0.05

Probability that insurance co has to pay more than 5000 = 5%

(24)P ( x>= 7000 / insurance co has already paid)

P ( x>= 7000 & insuranc co has paid) = 0.05

P( insurance co has already paid) = 0.25

P ( x>= 7000 / insurance co has already paid)  = 0.05 / 0.25 = 0.2

Insurance company has already paid a claim & the probability that the claim was at least \$7,000 = 20%

(25)

 x P(x) x* P(x) x square x 2* P(x) 0 0.75 0 0 0 2000 0.12 240 4000000 480000 10000 0.08 800 100000000 8000000 14000 0.04 560 196000000 7840000 20000 0.01 200 400000000 4000000 Total 1.00 1800 700000000 20320000

Mean = 1800

SD = 4132

var = 17073424

old var = 2066 * 2066 = 4268356

Hence 17073424 / 4268356 = 4

Mean will double and variance will increase 4 times.