Find ${\text{P}}(0 \leqslant X \leqslant 2)$.

Find ${\text{P}}(\left| X \right| > 1)$.

If ${\text{P}}(X > c) = 0.44$, find the value of $c$.

${\text{P}}(0 \leqslant X \leqslant 2) = 0.242$    (M1)A1

[2 marks]

METHOD 1

${\text{P}}(\left| X \right| > 1) = {\text{P}}(X <  - 1) + {\text{P}}(X > 1)$    (M1)

$= 0.02275 \ldots  + 0.84134 \ldots$    (A1)

$= 0.864$    A1

METHOD 2

${\text{P}}(\left| X \right| > 1) = 1 - {\text{P}}( - 1 < X < 1)$    (M1)

$= 1 - 0.13590 \ldots$    (A1)

$= 0.864$    A1

[3 marks]

$c = 3.30$    (M1)A1

[2 marks]

Part (a) was generally well done. In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.

Part (b) was not well done with many candidates not knowing what ${\text{P}}(\left| X \right| > 1)$ represents. In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.

In part (c), a number of candidates did not recognise that ${\text{P}}(X > c) = 1 - {\text{P}}(X \leqslant c)$. In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.