As risk manager, you are concerned about the additional liability exposure the firm will face

if it accepts a risky project. You obtain an estimate of the annual total loss distribution from

an insurance company that has many years of experience dealing with these types of

exposures. The annual total loss distribution is given below. The management team is

worried about how the potential liability losses will be financed. The company decides to

establish a loss reserve such that it can be $91\%$ confident that its actual losses can be met by

the fund. Determine the size of the required loss reserve using Chebychey's Theorem

and also the Normal Power Approximation. $($Birthday is $4/26/2003)$

Total Loss Distribution:

Mean $,$$$150,000$ if your birth month is Jan., Feb., or March

$$155,000$ if your birth month is April, May, or June

$$160,000$ if your birth month is July, Aug., or Sept.

$$165,000$ if your birth month is Oct., Nov., or Dec.

Std$.$ Dev. $,$$$40,000$ if your hirth day is $1-8$

$$45,000$ if your birth day is $9-17$

$$50,000$ if your birth day is $18-24$

$$55,000$ if your hirth day is $25-31$

Skewness Coefficient $1\mathrm{.}5$ if your birth year is $2004$ or later

$2\mathrm{.}0$ if your birth year is $2003$

$2\mathrm{.}5$ if your birth year if $2002$

$3\mathrm{.}0$ if your birth year is $2001$ or earlier

For example, for my birthdate of $10/20/1958,$ the total loss distribution has a mean of

$$165,000,$ a standard deviation of $$50,000,$ and a skewness coefficient of $3.$