Analysis and Approaches for IBDP Maths Ebook 1 | Page 289

94
Paper 2 Section A – Quartiles of a distribution
Front Page
Example
A random variable X is normally distributed with � � 70 and � � 6 . Find the
interquartile range of X .
Solution
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P( X �Q) � 0.25
(M1) for valid approach
1
Q1 � 65.9530615
(A1) for correct value
P( X �Q
) � 0.75
(M1) for valid approach
3
Q3 � 74.0469385
(A1) for correct value
The interquartile range of X
�Q3� Q1
(A1) for correct formula
�74.0469385 � 65.9530615
� 8.093876997
� 8.09
A1 N3
[6]
Exercise 94
1. A random variable X is normally distributed with � � 240 and � � 15. Find the
interquartile range of X .
2. A random variable X is normally distributed with � � 160 and � � 8. Find the
difference between the 70 th percentile and the 30 th percentile.
[6]
[6]
21
3. A random variable X is normally distributed with � � 88 and � � 4 . Find the difference
between the 90 th percentile and the 10 th percentile.
[6]
4. A random variable X is normally distributed with � � 50 and � � 3. The values s and
t , where s� t, are the data values that divide the whole distribution into 3 equal parts.
Find t� s.
[6]
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