QCAA Continuous Random Variables Mini Test 3
External Assessment Paper 2 — Technology-active
Number of marks: 9
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.
Calculate the expected value of a continuous random variable \(X\) with the probability density function
- (A) 1.72
- (B) 1.15
- (C) 1.00
- (D) 0.11
The mass (g) of adult kookaburras in a certain region is normally distributed with a mean of 300 g and a standard deviation of 13 g. Select the correct statement about the mass of adult kookaburras.
- (A) 34% are between 287 g and 313 g
- (B) 68% are between 274 g and 326 g
- (C) 95% are between 261 g and 326 g
- (D) 99.7% are between 261 g and 339 g
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.
The heights of students at School A are normally distributed with a mean of 165 cm and a standard deviation of 15 cm.
a) Determine the probability that a student chosen at random from School A is shorter than 180 cm. [1 mark]
b) Determine the minimum integer value of the height of a student who is in the top 2% of this distribution. [3 marks]
The heights of students at School B are also normally distributed. A student at School B has the same height as the height determined in Question 14b) but their corresponding z-score is 3.
c) Determine which student's height ranks higher in terms of percentile for their school. [3 marks]
END OF PAPER
