| Date | May 2016 | Marks available | 2 | Reference code | 16M.2.sl.TZ1.1 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Shade | Question number | 1 | Adapted from | N/A |
Question
A random variable \(X\) is distributed normally with a mean of 20 and standard deviation of 4.
On the following diagram, shade the region representing \({\text{P}}(X \leqslant 25)\).
Write down \({\text{P}}(X \leqslant 25)\), correct to two decimal places.
Let \({\text{P}}(X \leqslant c) = 0.7\). Write down the value of \(c\).
Markscheme
A1A1 N2
Note: Award A1 for vertical line clearly to right of mean,
A1 for shading to left of their vertical line.
\({\text{P}}(X \leqslant 25) = 0.894350\) (A1)
\({\text{P}}(X \leqslant 25) = 0.89\) (must be 2 d.p.) A1 N2
[2 marks]
\(c = 22.0976\)
\(c = 22.1\) A2 N2
[2 marks]
Examiners report
There was a mixed response to this question: candidates either very confidently answered each part, or were completely lost. Most were able to shade the correct region in part (a) and in part (b), answers were not always left to two decimal places. It was not uncommon to see candidates converting to standard normal form in part (c) before using their calculators, suggesting that they were not only unfamiliar with the meaning of the command term “write down” but were unclear as to what the given information was actually asking for.
There was a mixed response to this question: candidates either very confidently answered each part, or were completely lost. Most were able to shade the correct region in part (a) and in part (b), answers were not always left to two decimal places. It was not uncommon to see candidates converting to standard normal form in part (c) before using their calculators, suggesting that they were not only unfamiliar with the meaning of the command term “write down” but were unclear as to what the given information was actually asking for.
There was a mixed response to this question: candidates either very confidently answered each part, or were completely lost. Most were able to shade the correct region in part (a) and in part (b), answers were not always left to two decimal places. It was not uncommon to see candidates converting to standard normal form in part (c) before using their calculators, suggesting that they were not only unfamiliar with the meaning of the command term “write down” but were unclear as to what the given information was actually asking for.
