DATA:
Probability  Payment 
0.75  0 
0.12  1000 
0.08  5000 
0.04  7000 
0.01  10000 
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
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
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
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
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.
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