Company XYZ will pay a death benefit of $1000 to each of its 5000 employees who die in the upcoming year. There is 3% chance that an employee will die in the upcoming year.
Determine the amount of funds that Company XYZ needs to have if the company wants to have a 95% probability of having sufficient money to pay the benefits. (You may ignore the continuity correction.)
The number of employees who die out of the 5000 employees in the coming year could be modelled here as:
This can be approximated to a normal distribution here as:
From standard normal tables, we have here:
P(Z < 1.645) = 0.95
Therefore the amount of funds here is computed as:
= Mean + 1.645*Sd
Therefore the funds amount here is computed as:
= 169.84*$1000
= $169,842.55
Therefore $169,842.55 is the required amount of funds here
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