QCAA Maths Methods Discrete Random Variables Mini Test 3
External Assessment Paper 2 — Technology-active
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.
Consider the Bernoulli distribution where the outcomes for rolling a six-sided die are a four and not rolling a four. Determine the variance of the resulting Bernoulli distribution in this scenario.
- (A) 0.027˙
- (B) 0.138˙
- (C) 0.16
- (D) 0.83
The probability of hitting a target in a particular binomial experiment is (0.72). Determine the mean of the number of hits if this experiment is repeated eight times.
- (A) 1.61
- (B) 2.24
- (C) 5.76
- (D) 7.28
The probability of hitting a bullseye on a standard dartboard is 1 in 1250. What is the probability of hitting a bullseye exactly once in 10 attempts?
- (A) (binom{9}{1} times (frac{1}{1250})^1 times (frac{1249}{1250})^9)
- (B) (binom{9}{1} times (frac{1}{1250})^0 times (frac{1249}{1250})^1)
- (C) (binom{10}{1} times (frac{1}{1250})^1 times (frac{1249}{1250})^9)
- (D) (binom{10}{1} times (frac{1}{1250})^9 times (frac{1249}{1250})^1)
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.
A salesperson has a 20% probability of making a sale to each customer who enters the store. Each sale is independent of all other sales.
a) Determine the mean number of sales on a day where 25 customers enter the store. [2 marks]
b) Determine the standard deviation of the number of sales on a day where 25 customers enter the store. [2 marks]
c) Determine the minimum number of customers who would have to enter the store to have an 88% chance or more of making at least one sale. [3 marks]
END OF PAPER
