Date | November 2014 | Marks available | 4 | Reference code | 14N.1.hl.TZ0.9 |
Level | HL only | Paper | 1 | Time zone | TZ0 |
Command term | Find | Question number | 9 | Adapted from | N/A |
Question
A continuous random variable T has probability density function f defined by
f(t)={|2−t|,1≤t≤30,otherwise.
Sketch the graph of y=f(t).
Find the interquartile range of T.
Markscheme
|2−t| correct for [1, 2] A1
|2−t| correct for [2, 3] A1
EITHER
let q1 be the lower quartile and let q3 be the upper quartile
let d=2−q1 (=q3−2) and so IQR=2d by symmetry
use of area formulae to obtain 12d2=14
(or equivalent) M1A1
d=1√2 or the value of at least one q. A1
OR
let q1 be the lower quartile
consider ∫q11(2−t)dt=14 M1A1
obtain q1=2−1√2 A1
THEN
IQR=√2 A1
Note: Only accept this final answer for the A1.
[4 marks]
Total [6 marks]
Examiners report
The sketched graphs were mostly acceptable, but sometimes scrappy.
Most candidates had some idea about the upper and lower quartiles, but some were rather vague about how to calculate them for this probability density function. Even those who integrated for the lower quartile often made algebraic mistakes in calculating its value.