QCAA Maths Methods Paper 2 Statistics Mini Test 3
External Assessment Paper 2 — Technology-active
Number of marks: 10
Perusal time: 1 minute
Writing time: 15 minutes
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.
An online retailer claims that 90% of all orders are shipped within 12 hours of being received. On a particular day, 121 orders were received and 102 orders were shipped within 12 hours.
a) State the sample proportion of orders shipped within 12 hours. [1 mark]
The distribution of the sample proportion of all orders that are shipped within 12 hours of being received on any day is approximately normal.
b) Assuming the online retailer’s claim is true, find the probability that, in a random sample of 121, less than 85% of all orders are shipped within 12 hours. [3 marks]
c) Use the result from 13b) to evaluate the reasonableness of the online retailer’s claim. [2 marks]
A researcher found that 17 out of 50 randomly selected people had used public transport in the past week.
a) Determine the sample proportion of people who had used public transport in the past week. [1 mark]
b) Determine an approximate 95% confidence interval for the proportion of people who had used public transport in the past week. [2 marks]
c) Someone claims that: 50% of people use public transport each week.
Use your answer from Question 11b) to explain whether the data can or cannot support this claim. [1 mark]
END OF PAPER
