Analysis and Approaches for IBDP Maths Ebook 1 | Page 287

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Paper 2 Section A – Finding unknown parameters
Front Page
Example
Solution
A random variable X is normally distributed with � and � . It is given that 6% of the
data are less than 110, and 71% of the data are less than 140. Find the value of � and of
� .
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P( X �110) � 0.06
� 110 � � �
P�Z
� ��0.06
(M1) for standardization
� � �
110 � �
�� 1.554773593
(A1) for correct value
�
110 � � � � 1.554773593 �
� �110 � 1.554773593 � …(1) A1
P( X �140) � 0.71
� 140 � � �
P�Z
� ��0.71
� � �
140 � �
� 0.5533847152
�
(A1) for correct value
140 ��
� 0.5533847152 �
� �140 � 0.5533847152 � …(2) A1
(1) � (2)
�110 �1.554773593 � �140 � 0.5533847152 �
(M1) for setting equation
2.108158308 � � 30
� � 14.23043036
� �110 � 1.554773593(14.23043036)
� � 132.12509734
��
� 132 , � � 14.2
A2 N4
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