Find ${\rm{P}}(X \le 475)$ .

Given that ${\rm{P}}(X > a) = 0.27$ , find $a$.

evidence of attempt to find ${\rm{P}}(X \le 475)$     (M1)

e.g. ${\rm{P}}(Z \le 1.25)$

${\rm{P}}(X \le 475) = 0.894$     A1     N2

[2 marks]

evidence of using the complement     (M1)

e.g. 0.73, $1 - p$

$z = 0.6128$     (A1)

setting up equation     (M1)

e.g. $\frac{{a - 450}}{{20}} = 0.6128$

$a = 462$     A1     N3

[4 marks] 

It remains very clear that some centres still do not give appropriate attention to the normal distribution. This is a major cause for concern. Most candidates had been taught the topic but many had difficulty understanding the difference between $z$, $F(z)$, $a$ and $x$ . Very little working was shown which demonstrated understanding. Although the GDC was used extensively, candidates often worked with the wrong tail and did not write their answers correct to 3 significant figures.

It remains very clear that some centres still do not give appropriate attention to the normal distribution. This is a major cause for concern. Most candidates had been taught the topic but many had difficulty understanding the difference between $z$, $F(z)$, $a$ and $x$ . Very little working was shown which demonstrated understanding. Although the GDC was used extensively, candidates often worked with the wrong tail and did not write their answers correct to 3 significant figures.

Many candidates had trouble with part (b), a majority never found the complement, instead using their GDCs to calculate the result, which many times was finding a for $P(X \leqslant a) = 0.27$ instead of for $P(X \geqslant a) = 0.27$ . Many others substituted the values of $0.27$ or $0.73$ into the equation, instead of the $z$-scores.