2023 QCE Maths Methods Paper 1 Mini Test 4
External Assessment Paper 1 — Technology-free
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.
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.
Two random samples (A and B) were obtained using two different Bernoulli experiments. Each Bernoulli trial in the random samples was recorded as 1 (for success) or 0 (for failure). The results are shown.
| A | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| B | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
In sample A, for each trial the mean is 0.8 and the variance is 0.16.
a) Use the sample B results to determine the mean and variance for each trial in sample B. [2 marks]
b) Compare the variability about the means of samples A and B. [2 marks]
At a certain airport, the departure of one in five international flights is delayed every day. The status of any flight is independent of other flights.
One international flight is selected at random each day for three days. Each selection is recorded as either 'delayed' or 'not delayed'.
a) State two conditions that make this context suitable for modelling using a binomial random variable. [2 marks]
b) Calculate the probability that at least two of the selected flights were delayed. [3 marks]
END OF PAPER
