2022 MI P2 Q11
In this question you should, where applicable, state clearly all the distributions that you use, together with the values of the appropriate parameters.
The time spent by each customer at S Supermarket is denoted by the random variable $X$. $X$ follows a normal distribution with mean $a$ minutes and standard deviation $b$ minutes.
(i)
Given that $\text{P}\left( X>c \right)=0.3$, where $c$ is a constant. Find
(a) $\text{P}\left( a<X<c \right)$,
[1]
(b) $\text{P}\left( c<X<a+b \right)$.
[2]
Use $a=35$ and $b=10$ for the rest of this question.
Alice, Barry and Christine are three customers at S Supermarket who do not know each other. Find the probability that
(ii)
the time spent by Alice differs from the time spent by Barry by less than a minute,
[3]
(iii)
the total time spent by Barry and Christine exceeds twice the time spent by Alice by at least $15$ minutes,
[3]
(iv)
the total time spent by Alice, Barry and Christine at S Supermarket is at most $110$ minutes.
[3]
(v)
If Barry and Christine were members of the same family, what can you say about the validity of your answers in parts (ii), (iii) and (iv)?
[1]
Suggested Video Solutions
Our H2 Math Tuition includes
- Question Bank with Video solutions to 1400+ questions
- Online Portal
- H2 Math Summary Notes
- Structured Curriculum and Notes
Share with your friends!
Continue reading
Maximizing June Holidays: Is Joining a Crash Course Necessary?
As June holidays approach, students find themselves at a crucial juncture in their academic journey. With the semester winding down and exams looming on the horizon, the pressure to excel
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration