| Date | November 2016 | Marks available | 3 | Reference code | 16N.2.sl.TZ0.5 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
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 \(w\).
A newborn baby has a low birth weight.
Find the probability that the baby weighs at least 2.15 kg.
Markscheme
valid approach (M1)
eg\(\,\,\,\,\,\)\(z = - 1.61643\), 
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]
