Question

A normally distributed risk is described below.
Risk:		Auto losses
Mean:		300,000
Std. Dev.		50,000
What is the probability that losses will be below:
400,000

2

A normally distributed speculative risk is described below.
Risk:		Exchange rate losses
Mean:		50,000
Std. Dev.		100,000
What is the probability that losses will be below:
-50,000

3

A normally distributed risk is described below.
Risk:		Employee injuries
Mean:		2,000,000
The risk manager is 99.5% certain that losses will be below 3,000,000.
What is the std. dev. of this risk?

A normally distributed risk is described below.
Risk:	Fire losses
The risk manager is 99.5% certain that losses will be below 2,500,000.
The risk manager is 84% certain that losses will be below 2,000,000.

4

What is the mean of this risk?

5

What is the std. dev. Of this risk?

Answer 1

1. 97.725%

2. 15.8655%

3. 388224.5

4. Standard deviation = 316181.3

Mean = 1685571

Note that,

Z = (X – ?) / ?

Where,

Z is the standard normal variable

X is the random variable

? is the mean

? is the standard deviation

P1 and P2 are the probabilities.