QCAA Continuous Random Variables Mini Test 7
External Assessment Paper 2 — Technology-active
Number of marks: 4
Perusal time: 30 seconds
Writing time: 6 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.
The scores obtained on a test can be assumed to be normally distributed with a mean of 102 and a standard deviation of 19.
What proportion of scores are over 113?
- (A) 0.2813
- (B) 0.5789
- (C) 0.7187
- (D) 0.8216
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 random variable \(B\) is normally distributed with a mean of 0 and a standard deviation of 1.
Determine the probability that the quadratic equation \( x^2 + 3x + 2B = 0 \) has real roots.
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