Find ${\rm{P}}(X \le 22.9)$ .

Given that ${\rm{P}}(X < k) = 0.55$ , find the value of $k$ .

evidence of appropriate approach     (M1)

eg   $z = \frac{{22.9 - 20}}{5}$

$z = 0.58$     (A1)

${\rm{P}}(X \le 22.9) = 0.719$     A1     N3

[3 marks]

$z$-score for $0.55$ is $0.12566…$     (A1)

valid approach (must be with $z$-values)     (M1)

eg using inverse normal, $0.1257 = \frac{{k - 20}}{5}$

$k = 20.6$     A1     N3

[3 marks]

The normal distribution was handled better than in previous years with many candidates successful in both parts and very few blank responses. Some candidates used tables and $z$-scores while others used the GDC directly; the GDC approach earned full marks more often than the $z$-score approach.

The normal distribution was handled better than in previous years with many candidates successful in both parts and very few blank responses. Some candidates used tables and $z$-scores while others used the GDC directly; the GDC approach earned full marks more often than the $z$-score approach. A common error in part (b) was to set the expression for $z$-score equal to the probability. Many candidates had difficulty giving answers correct to three significant figures; this was particularly an issue if no working was shown.