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Date May 2019 Marks available 2 Reference code 19M.1.AHL.TZ1.H_6
Level Additional Higher Level Paper Paper 1 Time zone Time zone 1
Command term Find Question number H_6 Adapted from N/A

Question

Let X be a random variable which follows a normal distribution with mean μ . Given that  P ( X < μ 5 ) = 0.2  , find

P ( X > μ + 5 ) .

[2]
a.

P ( X < μ + 5 | X > μ 5 ) .

[5]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

use of symmetry eg diagram       (M1)

P ( X > μ + 5 ) = 0.2        A1

[2 marks]

a.

EITHER

P ( X < μ + 5 | X > μ 5 ) = P ( X > μ 5 X < μ + 5 ) P ( X > μ 5 )        (M1)

       = P ( μ 5 < X < μ + 5 ) P ( X > μ 5 )        (A1)

       = 0.6 0.8       A1A1

Note: A1 for denominator is independent of the previous A marks.

OR

use of diagram       (M1)

Note: Only award (M1) if the region  μ 5 < X < μ + 5 is indicated and used.

P ( X > μ 5 ) = 0.8        P ( μ 5 < X < μ + 5 ) = 0.6        (A1)

Note: Probabilities can be shown on the diagram.

= 0.6 0.8       M1A1

THEN

= 3 4 = ( 0.75 )       A1

[5 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability

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