Q11 · 2023 · Technology-freeSimple familiar4 marks
QUESTION 11 (4 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.
| Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 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)[2 marks]
Use the sample B results to determine the mean and variance for each trial in sample B.
b)[2 marks]
Compare the variability about the means of samples A and B.
WORKED SOLUTION
4 marksQCAA guide · typeset solution
ANSWER
a) Mean , variance . b) Sample B has more variability about its mean than sample A.
Worked solution
a) Sample B:
b) Sample B has a larger variance than sample A. Because sample B has the larger variance, it has more variability about the mean compared to sample A.
correctly determines the mean for sample B
determines the variance for sample B
identifies that sample B has the larger variance
provides reasoning that explains that larger variance indicates larger variability
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