Analysis and Approaches for IBDP Maths Ebook 1 | Page 292

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3. A random variable X is normally distributed with mean 15. The standard deviation of
X is � . It is given that 35% of the data are greater than 15 and less than 20.
(a) Find P( X � 10) .
(b) Find the value of � .
The random variable Y is normally distributed with mean � and standard
deviation 1.9. The events X � 10 and Y � 10 are independent, and
P(( X �10) �( Y �10)) � 0.075 .
(c) Find � .
(d) Given that Y � 10 , find P(11 �Y
� 12) .
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[3]
[5]
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4. A random variable X is normally distributed with mean 200. The standard deviation of
X is � . It is given that 40% of the data are greater than 200 and less than 240.
(a) Find the value of � .
The random variable Y is normally distributed with mean � and standard
deviation s . The events X � 240 and Y � 240 are independent, and
P(( X � 240) �( Y � 240)) � 0.01 . It is also given that
P((200 � X � 240) �(200 � Y � 240)) � 0.2 .
(b) Find the value of � and of s .
(c) Given that 200 �Y
� 240 , find P( Y � 220) .
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