Apps. and Interpretation for IBDP Maths Ebook 1 | Page 312

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Solution
(a) (i) Let H : Height of a tree in the park
The required probability
�P( H � 52.5)
(M1) for valid approach
(b)
� 0.105649839
� 0.106
A1 N2
(ii) P( H �50 | H � 52.5)
(R1) for correct probability
P( H � 50 � H � 52.5)
�
P( H � 52.5)
P( H � 50)
�
P( H � 52.5)
(A1) for correct formula
0.0477903304
�
0.105649839
(A1) for correct values
� 0.4523464571
� 0.452
A1 N4
The required probability
� P( H � 52.5) �P( H � 52.5)
(M1) for valid approach
�0.105649839 � 0.105649839
� 0.0111618885
� 0.0112
A1 N2
(c) (i) The required expected number
� (80)(0.105649839)
(A1) for correct formula
� 8.45198712
� 8.45
A1 N2
[6]
[2]
(ii)
Let X : Number of short trees in the
selected sample
X ~ B (80, 0.105649839)
(R1) for binomial distribution
The required probability
�P( X � 11)
(M1) for valid approach
�P( X � 10)
(A1) for correct value
� 0.7784376955
� 0.778
A1 N4
[6]
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