Question

Under a particular insurance policy, claim amounts are modelled as having a normal distribution with standard deviation of €100. The claims are assumed to be independent of each other. Two claims are selected at random. Calculate the probability that the difference between the claim amounts will be greater than €300.

Answer 1

Let the claims be A and B.

A is normal distributed with mean and Standard Deviation 100

B is normal distributed with mean and Standard Deviation 100

So,by Theorem:
X= A - B normal distributed with mean 0   and Standard Deviation

To find P(X>300):

Z = (300 - 0)/141.4214

= 2.1213

By Technology, Cumulative Area Under Standard Normal Curve = 0.9831

So,

P(X>300) =1 -0.9831 = 0.0169

So,

Answer is:

0.0169