Processing math: 100%

User interface language: English | Español

Date May 2016 Marks available 2 Reference code 16M.2.hl.TZ2.2
Level HL only Paper 2 Time zone TZ2
Command term Find Question number 2 Adapted from N/A

Question

A random variable X is normally distributed with mean 3 and variance 22.

Find P(0X2).

[2]
a.

Find P(|X|>1).

[3]
b.

If P(X>c)=0.44, find the value of c.

[2]
c.

Markscheme

P(0X2)=0.242    (M1)A1

[2 marks]

a.

METHOD 1

P(|X|>1)=P(X<1)+P(X>1)    (M1)

=0.02275+0.84134    (A1)

=0.864    A1

METHOD 2

P(|X|>1)=1P(1<X<1)    (M1)

=10.13590    (A1)

=0.864    A1

[3 marks]

b.

c=3.30    (M1)A1

[2 marks]

c.

Examiners report

Part (a) was generally well done. In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.

a.

Part (b) was not well done with many candidates not knowing what P(|X|>1) represents. In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.

b.

In part (c), a number of candidates did not recognise that P(X>c)=1P(Xc). In each question part, a number of candidates could have benefited from producing a labelled sketch of the situation.

c.

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.7 » Normal distribution.
Show 52 related questions

View options