Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js

User interface language: English | Español

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)={|2t|,1t30,otherwise.

Sketch the graph of y=f(t).

[2]
a.

Find the interquartile range of T.

[4]
b.

Markscheme

|2t| correct for [1, 2]     A1

|2t| correct for [2, 3]     A1

a.

EITHER

let q1 be the lower quartile and let q3 be the upper quartile

let d=2q1 (=q32) and so IQR=2d by symmetry

use of area formulae to obtain 12d2=14

(or equivalent)     M1A1

d=12 or the value of at least one q.     A1

OR

let q1 be the lower quartile

consider q11(2t)dt=14     M1A1

obtain q1=212     A1

THEN

IQR=2     A1

 

Note:     Only accept this final answer for the A1.

[4 marks]

Total [6 marks]

b.

Examiners report

The sketched graphs were mostly acceptable, but sometimes scrappy.

a.

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.

b.

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.5 » Definition and use of probability density functions.
Show 25 related questions

View options