Draw a diagram that shows this information.

Write down the probability that a randomly chosen candidate who sat the Chemistry examination scored at most 60 marks.

Hee Jin scored 80 marks in the Chemistry examination.

Find the probability that a randomly chosen candidate who sat the Chemistry examination scored more than Hee Jin.

The candidates’ marks in the Physics examination are normally distributed with a mean of $63$ and a standard deviation of $10$. Hee Jin also scored $80$ marks in the Physics examination.

Find the probability that a randomly chosen candidate who sat the Physics examination scored less than Hee Jin.

The candidates’ marks in the Physics examination are normally distributed with a mean of $63$ and a standard deviation of $10$. Hee Jin also scored $80$ marks in the Physics examination.

Determine whether Hee Jin’s Physics mark, compared to the other candidates, is better than her mark in Chemistry. Give a reason for your answer.

To obtain a “grade A” a candidate must be in the top $10\%$ of the candidates who sat the Physics examination.

Find the minimum possible mark to obtain a “grade A”. Give your answer correct to the nearest integer.

     (A1)(A1)

Notes: Award (A1) for rough sketch of normal curve centred at $60$, (A1) for some indication of $12$ as the standard deviation eg, as diagram, or with $72$ and $48$ shown on the horizontal axis in appropriate places, or for $96$ and $24$ shown on the horizontal axis in appropriate places.

[2 marks]

$0.5 \left( {\frac{1}{2},{\text{ 50% }}} \right)$     (A1)

Note: Accept only the exact answer.

[1 mark]

$0.0478{\text{ }} (0.0477903...)$     (G2)

Note: Award (G1) for $0.952209…$, award (M1)(G0) for diagram with correct area shown but incorrect answer.

[2 marks]

$0.955 {\text{ }} (0.955434...)$     (G2)

Note: Award (G1) for $0.044565…$, award (M1)(G0) for diagram with correct area shown but incorrect answer.

[2 marks]

$0.0446 < 0.0478$     (R1)

Notes: Award (R1) for correct comparison seen. Accept alternative methods, for example, $1–$ (their answer to part (c)) used in comparison or a comparison based on $z$ scores.

the Physics result is better     (A1)(ft)

Notes: Do not award (R0)(A1). Follow through from their answers to part (c) and part (d).

[2 marks]

$76$     (G3)

Notes: Award (G1) for $75.8155…$, award (G2) for $75$.

     Award (M1)(G0) for diagram with correct area shown but incorrect answer.

[3 marks]