Apps. and Interpretation for IBDP Maths Ebook 1 | Page 306

Your Practice Set – Applications and Interpretation for IBDP Mathematics
87
Paper 1 – Critical Values in a Normal Distribution
Example
A random variable X is distributed normally with a mean of 100 and standard deviation
of 5.
(a) On the following diagram, shade the region representing P( X � 97) .
[2]
(b) Write down P( X � 97) , correct to four decimal places.
(c) Let P( X �c) � 0.4 . Write down the value of c .
[2]
[2]
Solution
(a) For vertical line clearly to the left of the mean A1
For shading to the left of the vertical line A1 N2
[2]
(b) P( X �97) � 0.2742530646
(A1) for correct value
P( X �97) � 0.2743
A1 N2
(c) c � 98.73326449
c � 98.7
A2 N2
[2]
[2]
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