QCAA Maths Methods Discrete Random Variables Mini Test 1
External Assessment Paper 1 — Technology-free
Number of marks: 6
Perusal time: 30 seconds
Writing time: 9minutes
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.
The table shows the time a technician has spent servicing photocopiers.
| Time (in minutes) | Frequency |
|---|---|
| \(0 \le t < 5\) | 10 |
| \(5 \le t < 10\) | 20 |
| \(10 \le t < 15\) | 30 |
| \(15 \le t < 20\) | 40 |
What is the probability that a given service required at least 10 minutes but less than 20 minutes?
- (A) 0.15
- (B) 0.35
- (C) 0.70
- (D) 0.85
A test includes six multiple choice questions. Each question has four options for the answer. If the answers are guessed, the probability of getting at most two questions correct is represented by
- (A) \(\binom{6}{0}0.25^0 \times 0.75^6 + \binom{6}{1}0.25^1 \times 0.75^5\)
- (B) \(\binom{6}{0}0.25^0 \times 0.75^6 + \binom{6}{1}0.25^1 \times 0.75^5 + \binom{6}{2}0.25^2 \times 0.75^4\)
- (C) \(1 - \left( \binom{6}{0}0.25^0 \times 0.75^6 + \binom{6}{1}0.25^1 \times 0.75^5 \right)\)
- (D) \(1 - \left( \binom{6}{0}0.25^0 \times 0.75^6 + \binom{6}{1}0.25^1 \times 0.75^5 + \binom{6}{2}0.25^2 \times 0.75^4 \right)\)
If the probability of success in a Bernoulli trial is 0.30, the variance is
- (A) 0.70
- (B) 0.46
- (C) 0.30
- (D) 0.21
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.
In any five-day working week Leonardo either catches a bus to work or uses another form of transportation. On average, he catches the bus to work on three of the five days. His decision on any given day is independent of his decision on any other day.
Determine the probability that Leonardo catches a bus to work on exactly one day in a given five-day working week.
END OF PAPER
