Question

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

Answer 1

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.