Question

The amount of a loss, Y, is assumed to follow a Normal distribution with a mean of ? and

a variance of ?^2. The median of Y is 56.5 and the 59.1-th percentile of Y is 56.776.

Determine P(Y > 60 ).

Answer 1

Let ,

Given : Median=56.5 and 59.1-th percentile is 56.776

For normal distribution , Median=mean==56.5

Now , the 59.1-th percentile is ,

...............(I)

From standard normal distribution table,

..................(II)

From (I) and (II) , we get ,

Now ,

; From standard normal distribution table