A question is this type if and only if it involves finding the probability for a process with 3+ independent stages where times/amounts are normally distributed (e.g. triathlon, multi-stage journey, game rounds).
17 questions · Standard +0.6
| Mean | Standard deviation | |
| Mowing | 44 | 4.8 |
| Hoeing | 32 | 2.6 |
| Pruning | 21 | 3.7 |
| Mean |
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| Swimming | 11.07 | 2.36 | ||
| Cycling | 57.33 | 8.76 | ||
| Running | 24.23 | 3.75 |
| Type of round | Mean | Standard deviation |
| Starter | 200 | 15 |
| Middle | 220 | 25 |
| Final | 250 | 20 |
| END |
| mean | standard deviation | |
| \(1 ^ { \text {st } }\) leg \(- A\) | 63.1 | 1.2 |
| \(2 ^ { \text {nd } }\) leg \(- B\) | 65.7 | 1.5 |
| \(3 ^ { \text {rd } } \operatorname { leg } - C\) | 65.4 | 1.8 |
| \(4 ^ { \text {th } }\) leg - \(D\) | 62.5 | 0.9 |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | Mean | Standard deviation |
| Washing | 35 | 2.4 |
| Drying | 46 | 3.1 |
| Folding | 12 | 2.2 |
| Section | Mean | Standard deviation |
| \(A\) | 264 | 13 |
| \(B\) | 173 | 9 |
| \(C\) | 264 | 13 |
| Question | Answer | Mark | AO | Guidance | ||||||
| \multirow[t]{3}{*}{1} | \multirow[t]{3}{*}{(a)} |
| M1 | 1.1a | Normal, mean \(\mu _ { A } + \mu _ { B } + \mu _ { C }\) | \multirow{3}{*}{} | ||||
| A1 | 1.1 | Variance 419 | ||||||||
| \(\mathrm { P } ( > 720 ) = 0.176649\) | A1 | 1.1 | Answer, 0.177 or better, www | |||||||
| \multirow[t]{2}{*}{1} | \multirow[t]{2}{*}{(b)} | \(2 A + B \sim \mathrm {~N} ( 701,757 )\) | M1 | 1.1a | Normal, same mean, \(4 \sigma _ { A } { } ^ { 2 } + \sigma _ { B } { } ^ { 2 }\) | \multirow{2}{*}{} | ||||
| \(\mathrm { P } ( > 720 ) = 0.244919\) | A1 [2] | 1.1 | Answer, art 0.245 | |||||||
| \multirow{2}{*}{2} | \multirow{2}{*}{(a)} | \(\frac { { } ^ { 8 } C _ { 3 } \times { } ^ { 20 } C _ { 5 } } { { } ^ { 28 } C _ { 8 } }\) | M1 A1 | 3.1b 1.1 | (Product of two \({ } ^ { n } C _ { r }\) ) ÷ \({ } ^ { n } C _ { r }\) At least two \({ } ^ { n } C _ { r }\) correct | \multirow[t]{2}{*}{Or \(\frac { 8 } { 28 } \times \frac { 7 } { 27 } \times \frac { 6 } { 26 } \times \frac { 20 } { 25 } \times \ldots \times \frac { 16 } { 21 } \times { } ^ { 8 } C _ { 3 } = 0.27934 \ldots\)} | ||||
| \(\frac { 56 \times 15504 } { 3108105 } = 0.27934 \ldots\) | A1 [3] | 1.1 | Any exact form or awrt 0.279 | |||||||
| 2 | (b) |
| M1 A1 | 3.1b 2.1 |
| Or, e.g. find \({ } _ { 12 } \mathrm { C } _ { 4 }\) - (\# (all separate) +\#(all together) \(+ \# ( 2,1,1 ) \times 3 +\) \#(2,2)) | ||||
| M1 | 1.1 | |||||||||
| A1 | 1.1 | |||||||||
| [4] | ||||||||||
| Question | Answer | Mark | AO | Guidance | |||||
| \multirow{7}{*}{3} | \multirow{7}{*}{(a)} | \(\mathrm { H } _ { 0 } : \mu = 700\) | B2 | 1.1 | One error, e.g. no or wrong | Ignore failure to define \(\mu\) | |||
| \(\mathrm { H } _ { 1 } : \mu < 700\) where \(\mu\) is the mean reaction | 1.1 | letter, \(\neq\), etc : B1 | here | ||||||
| \(\bar { x } = 607\) | M1 | 3.3 | Find sample mean | ||||||
| \(z = - 1.822\) or \(p = 0.0342\) or \(\mathrm { CV } = 616.05 \ldots\) | A1 | 3.4 | Correct \(z , p\) or CV | ||||||
| \(z < - 1.645\) or \(p < 0.05\) or \(607 < \mathrm { CV }\) | A1 | 1.1 | Correct comparison | ||||||
| Reject \(\mathrm { H } _ { 0 }\) | M1ft | 1.1 | Correct first conclusion | Needs correct method, like- | |||||
| Significant evidence that mean reaction times | A1ft | 2.2b | Context, not too definite (e.g. not "international athletes' reaction times are shorter" | ft on their \(z , p\) or CV | |||||
| 3 | (b) | (i) | Uses more information (e.g. magnitudes of differences) | B1 [1] | 2.4 | ||||
| \multirow{5}{*}{3} | \multirow{5}{*}{(b)} | \multirow{5}{*}{(ii)} | \(\mathrm { H } _ { 0 } : m = 700 , \mathrm { H } _ { 1 } : m < 700\) where \(m\) is the median reaction time for all international athletes | B1 | 2.5 | Same as in (i) but different letter or "median" stated | |||
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| For both, and \(T\) correct | |||||||||
| \(n = 6 , \mathrm { CV } = 2\) | A1 | 1.1 | Correct CV | ||||||
| Do not reject \(\mathrm { H } _ { 0 }\). Insufficient evidence that median reaction times of international athletes are shorter | A1ft [6] | 2.2b | In context, not too definite | FT on their \(T\) | |||||
| 3 | (c) | They use different assumptions | B1 [1] | 2.3 | Not "one is more accurate" | ||||
| Question | Answer | Mark | AO | Guidance | |||||||||||||||||||||||||||||||||
| 4 | (a) | \(\begin{aligned} | \int _ { 0 } ^ { a } x \frac { 2 x } { a ^ { 2 } } d x = 4 | ||||||||||||||||||||||||||||||||||
| { \left[ \frac { 2 x ^ { 3 } } { 3 a ^ { 2 } } \right] = 4 } | |||||||||||||||||||||||||||||||||||||
| \frac { 2 } { 3 } a = 4 \Rightarrow a = 6 \end{aligned}\) |
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| 4 | (b) |
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