18N.1.SL.TZ0.T_14

pestleMathematicsAISLPaper 118N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

The marks achieved by students taking a college entrance test follow a normal distribution with mean 300 and standard deviation 100.

In this test, 10 % of the students achieved a mark greater than k.

Marron College accepts only those students who achieve a mark of at least 450 on the test.

Find the value of k.

[2]

Find the probability that a randomly chosen student will be accepted by Marron College.

[2]

Given that Naomi attends Marron College, find the probability that she achieved a mark of at least 500 on the test.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(M1)

Note: Award (M1) for diagram that shows the correct shaded area and percentage, k has to be greater than the mean.

Award (M1) for P(mark > k) = 0.1 or P(mark ≤ k) = 0.9 seen.

428 (428.155…) (A1) (C2)

[2 marks]

(M1)

Note: Award (M1) for diagram that shows the correct shaded area and the value 450 labelled to the right of the mean.

Award (M1) for P(mark ≥ 450) seen.

0.0668 (0.0668072…, 6.68 %, 6.68072… %) (A1) (C2)

[2 marks]

$\frac{{0.0228}}{{0.0668}}$ $\left( {\frac{{0.0227500 \ldots }}{{0.0668072 \ldots }}} \right)$ (M1)

Note: Award (M1) for 0.0228 (0.0227500…) seen. Accept 1 − 0.97725.

= 0.341 (0.340532…, 34.1 %, 34.0532…%) (A1)(ft) (C2)

Note: Follow through from part (b), provided answer is between zero and 1.

[2 marks]

Examiners’ report

[N/A]