16N.2.SL.TZ0.S_5

pestleMathematicsAISLPaper 216N· sl-4-9-normal-distribution-and-calculationssource ↗

The weights, $W$ , of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than $w$ kg.

Given that 5.3% of newborn babies have a low birth weight, find $w$ .

[3]

A newborn baby has a low birth weight.

Find the probability that the baby weighs at least 2.15 kg.

[3]

Markscheme / solution

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

valid approach (M1)

eg $\,\,\,\,\,$ $z = - 1.61643$ , N16/5/MATME/SP2/ENG/TZ0/05.a/M

2.48863

$w = 2.49{\text{ (kg)}}$ A2 N3

[3 marks]

correct value or expression (seen anywhere)

eg $\,\,\,\,\,$ $0.053 - {\text{P}}(X \leqslant 2.15),{\text{ }}0.039465$ (A1)

evidence of conditional probability (M1)

eg $\,\,\,\,\,$ $\frac{{{\text{P}}(2.15 \leqslant X \leqslant w}}{{{\text{P}}(X \leqslant w)}},{\text{ }}\frac{{0.039465}}{{0.053}}$

0.744631

0.745 A1 N2

[3 marks]

Examiners’ report

[N/A]