Question

It has determined that a funded reserve is its preferred method of retention and it would like to make sure that it has enough to cover losses in 97.5% (2.5% on each side of the distribution) of all situations with losses normally distributed. How much does the retailer need to have in its funded reserve if the expected losses are $2.5m and standard deviation is $500k?

Answer 1

Given: 97.5% losses cover => probability of 0.975
   Z Score for 0.975 (from Z table) = 1.96

Expected Loss,μ= $2.5m
Standard Deviation,σ= $0.5m
Also,

Z=(x-μ)/σ
=> 1.96=(x-2.5)/0.5

=> x=$3.48m
Therefore, the retailer need to have $3.48m in its funded reserve.