Apps. and Interpretation for IBDP Maths Ebook 1 | Page 303

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Paper 1 – Symmetric Properties of a Normal Curve
Example
The random variable X is normally distributed with a mean of 45. The following
diagram shows the normal curve for X .
Let R be the shaded region under the curve, to the left of 35. The area of R is 0.18.
(a) Write down P( X � 35) .
(b) Find P(35 � X � 45) .
(c) Find P(45 � X � 55) .
[1]
[3]
[2]
Solution
21
(a) P( X �35) � 0.18
A1 N1
(b) P(35 � X � 45)
� P( X � 45) � P( X � 35)
(M1) for valid approach
�0.5 � 0.18
(A1) for substitution
� 0.32
A1 N3
(c) P(45 � X � 55)
� P(35 � X � 45)
(M1) for symmetric property
� 0.32
A1 N2
[1]
[3]
[2]
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