RVHS Term 3 Time Practice Q1

Timothy Gan

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]

Suggested Handwritten and Video Solutions

Students Only

Login here to view
Join Us

Our H2 Math Tuition includes

  • Question Bank with Video solutions to 1400+ questions
  • Online Portal
  • H2 Math Summary Notes
  • Structured Curriculum and Notes
Free Stuff

Share with your friends!

WhatsApp
Telegram
Facebook

Published: 27th July 2022

Written by

Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.

Leave a Reply

Your email address will not be published. Required fields are marked *