Find \({\rm{P}}(X > 27)\) .

Find the standard deviation of X .

symmetry of normal curve     (M1)

e.g. \({\rm{P}}(X < 25) = 0.5\)

\({\rm{P}}(X > 27) = 0.2\)     A1     N2

[2 marks]

METHOD 1

finding standardized value     (A1)

e.g. \(\frac{{27 - 25}}{\sigma }\)

evidence of complement     (M1)

e.g. \(1 - p\) , \({\rm{P}}(X < 27)\) , 0.8

finding z-score     (A1)

e.g. \(z = 0.84 \ldots \)

attempt to set up equation involving the standardized value     M1

e.g. \(0.84 = \frac{{27 - 25}}{\sigma }\) , \(0.84 = \frac{{X - \mu }}{\sigma }\)

\(\sigma = 2.38\)     A1     N3

METHOD 2

set up using normal CDF function and probability     (M1)

e.g. \({\rm{P}}(25 < X < 27) = 0.3\) , \({\rm{P}}(X < 27) = 0.8\)

correct equation     A2

e.g. \({\rm{P}}(25 < X < 27) = 0.3\) , \({\rm{P}}(X > 27) = 0.2\)

attempt to solve the equation using GDC     (M1)

e.g. solver, graph, trial and error (more than two trials must be shown)

\(\sigma = 2.38\)     A1     N3

[5 marks]

This question proved challenging for many candidates. A surprising number did not use the symmetry of the normal curve to find the probability required in (a). While many students were able to set up a standardized equation in (b), far fewer were able to use the complement to find the correct z-score. Others used 0.8 as the z-score. A common confusion when approaching parts (a) and (b) was whether to use a probability or a z-score. Additionally, many candidates seemed unsure of appropriate notation on this problem which would have allowed them to better demonstrate their method.

This question proved challenging for many candidates. A surprising number did not use the symmetry of the normal curve to find the probability required in (a). While many students were able to set up a standardized equation in (b), far fewer were able to use the complement to find the correct z-score. Others used 0.8 as the z-score. A common confusion when approaching parts (a) and (b) was whether to use a probability or a z-score. Additionally, many candidates seemed unsure of appropriate notation on this problem which would have allowed them to better demonstrate their method.