19N.2.AHL.TZ0.H_7

pestleMathematicsAAHLPaper 219N· sl-4-9-normal-distribution-and-calculationssource ↗

Runners in an athletics club have season’s best times for the 100 m, which can be modelled by a normal distribution with mean 11.6 seconds and standard deviation 0.8 seconds. To qualify for a particular competition a runner must have a season’s best time of under 11 seconds. A runner from this club who has qualified for the competition is selected at random. Find the probability that he has a season’s best time of under 10.7 seconds.

Markscheme / solution

$T \sim {\text{N}}\left( {11.6{\text{, }}{{0.8}^2}} \right)$

${\text{P}}\left( {T < \left. {10.7} \right|T < 11} \right)$ (M1)

$= \frac{{{\text{P}}\left( {T < 10.7 \cap T < 11} \right)}}{{{\text{P}}\left( {T < 11} \right)}}$ (M1)

$= \frac{{{\text{P}}\left( {T < 10.7} \right)}}{{{\text{P}}\left( {T < 11} \right)}}$ (M1)

${\text{P}}\left( {T < 10.7} \right) = 0.1302 \ldots$ (A1)

${\text{P}}\left( {T < 11} \right) = 0.2266 \ldots$ (A1)

${\text{P}}\left( {T < \left. {10.7} \right|T < 11} \right) = 0.575$ A1

Note: Accept only 0.575.

[6 marks]

Examiners’ report

[N/A]