| Date | November 2014 | Marks available | 2 | Reference code | 14N.1.sl.TZ0.12 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 12 | Adapted from | N/A |
Question
The daily January temperature of Cairns is normally distributed with a mean of 34°C and a standard deviation of 3.
Calculate the probability that the temperature on a randomly chosen day in January is less than 39°C.
Calculate the expected number of days in January that the temperature will be more than 39°C.
On a randomly chosen day in January, the probability that the temperature is above \(T\) °C is 0.7.
Find the value of \(T\).
Markscheme
(M1)
Note: Award (M1) for correctly shaded area.
\(0.952{\text{ }}(95.2\% ,{\text{ }}0.952209 \ldots )\) (A1) (C2)
\(31 \times (1 - 0.952209)\) (M1)
Note: Award (M1) for multiplying \(31\) by \(\left( {1 - {\text{ their answer to part (a)}}} \right)\).
\( = 1.48{\text{ }}(1.48150 \ldots )\) (A1)(ft) (C2)
Note: Follow through from part (a).
(M1)
Note: Award (M1) for correctly shaded area.
\(32.4{\text{ }}(32.4267 \ldots )\) (A1) (C2)
