QCAA Continuous Random Variables Mini Test 4
External Assessment Paper 2 — Technology-active
Number of marks: 10
Perusal time: 1 minute
Writing time: 15 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
A student is trying to determine which subject they performed best in compared to other students. Results from recent tests in four subjects (A to D) are shown. Assume student results in each subject are normally distributed.
In which subject did the student perform best compared to other students?
| Class mean | Class standard deviation |
Student's result |
|
|---|---|---|---|
| (A) | 62 | 22 | 77 |
| (B) | 55 | 25 | 74 |
| (C) | 61 | 15 | 70 |
| (D) | 73 | 20 | 82 |
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
Model bridges were constructed for a competition. The models that could support the heaviest loads before collapsing were given awards.
The load results of the competition were normally distributed, with a mean of 1.36 kg and a standard deviation of 0.12 kg.
Three award categories were used: honours for the top 15% of load results; distinction for the next 15%; and commendation for the next 15%.
The model bridge constructed by Finley only just missed out on a commendation. Kirby's model bridge only just qualified for honours. Determine the difference, to the nearest gram, between the loads supported by Finley and Kirby's models.
The time spent waiting in a queue at a certain supermarket is given by (\(X + 11\)) minutes, where \(X\) is a random variable with the probability density function \[ f(x) = \begin{cases} \frac{a(4-x^2)}{32}, & -2 \le x \le 2 \\ 0, & \text{otherwise} \end{cases} \]
Determine the probability of waiting between 10 and 12 minutes in a queue at this supermarket.
END OF PAPER
