Apps. and Interpretation for IBDP Maths Ebook 1 | Page 309

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Paper 1 – Quartiles of a Normal Distribution
Example
A random variable X is normally distributed with � � 70 and � � 6 .
(a) Find the lower quartile of X .
(b) Find the upper quartile of X .
(c) Hence, find the interquartile range of X .
[2]
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Solution
(a) P( X �Q1
) � 0.25
(M1) for valid approach
Q1 � 65.9530615
Thus, the lower quartile is 66.0. A1 N2
(b) P( X �Q3
) � 0.75
(M1) for valid approach
(c)
Q3 � 74.0469385
Thus, the upper quartile is 74.0. A1 N2
The interquartile range of X
�Q
� Q
(A1) for correct formula
3 1
�74.0469385 � 65.9530615
� 8.093876997
� 8.09
A1 N2
[2]
[2]
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