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.