RVHS Term 3 Time Practice Q1
From past records, the number of days of hospitalization for an individual with minor ailment can be modelled by a discrete random variable with probability density function given by
$\text{P}(X=x)=\left\{ \begin{matrix}
\frac{6-x}{15},\,\,\,\text{for}\,\,x=1,2,3,4,5 \\
0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\
\end{matrix} \right.$
An insurance policy pays $\$100$ per day for up to $3$ days of hospitalization and $\$25$ per day of hospitalization thereafter.
(i)
Calculate the expected payment for hospitalization for an individual for an individual under this policy.
[4]
(ii)
The insurance company will incur a loss if the total payout for $100$ hospitalization claims under this policy exceeds $\$24000$. Using a suitable approximation, estimate the probability that the insurance company will incur a loss for $100$ such claims.
[4]
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