Analysis and Approaches for IBDP Maths Ebook 1 | Page 291

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(d) P( Y �33| Y � 30)
P( Y � 33�Y
� 30)
�
P( Y � 30)
(M1) for valid approach
P(30 �Y
�33)
�
0.5
(A2) for correct values
0.4954555623
�
0.5
(A1) for correct value
� 0.9909111246
� 0.991
A1 N3
[5]
Exercise 95
1. A random variable X is normally distributed with mean, � . The standard deviation of
X is 2. It is given that 45% of the data are greater than � and less than 102.
(a) Find P( X � 102) .
(b) Find the value of � .
The random variable Y is normally distributed with mean � and standard
deviation 3. The events X � 102 and Y � 102 are independent, and
P(( X �102) �( Y �102)) � 0.475 .
(c) Find � .
(d) Given that Y � 102 , find P( Y � 100) .
[2]
[3]
[5]
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21
2. A random variable X is normally distributed with mean, � . The standard deviation of
X is 4.5. It is given that 78% of the data are greater than 70.
(a) Find P( X � 70) .
(b) Find the value of � .
The random variable Y is normally distributed with mean 80 and standard
deviation � . The events X � 70 and Y � 70 are independent, and
P(( X � 70) �( Y � 70)) � 0.0484 .
(c) Find � .
(d) Given that Y � 70 , find P( Y � 67) .
[2]
[3]
[5]
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