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.