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Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ2.S_3
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Write down Question number S_3 Adapted from N/A

Question

The random variable X is normally distributed with a mean of 100. The following diagram shows the normal curve for X .

M17/5/MATME/SP1/ENG/TZ2/03

Let R be the shaded region under the curve, to the right of 107. The area of R is 0.24.

Write down P ( X > 107 ) .

[1]
a.

Find P ( 100 < X < 107 ) .

[3]
b.

Find P ( 93 < X < 107 ) .

[2]
c.

Markscheme

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

P ( X > 107 ) = 0.24 ( = 6 25 ,   24 % )     A1     N1

[1 mark]

a.

valid approach     (M1)

eg P ( X > 100 ) = 0.5 ,  P ( X > 100 ) P ( X > 107 )

correct working     (A1)

eg 0.5 0.24 ,   0.76 0.5

P ( 100 < X < 107 ) = 0.26 ( = 13 50 ,   26 % )     A1     N2

[3 marks]

b.

valid approach     (M1)

eg 2 × 0.26 ,   1 2 ( 0.24 ) ,  P ( 93 < X < 100 ) = P ( 100 < X < 107 )

P ( 93 < X < 107 ) = 0.52 ( = 13 25 ,   52 % )     A1 N2

[2 marks]

c.

Examiners report

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

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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