Analysis and Approaches for IBDP Maths Ebook 1 | Page 294

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b) 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
[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 N2
[6]
Exercise 96
1. The weights of fish in a lake are normally distributed with a mean of 740 g and standard
deviation 46 g. Fishes are classified as big fishes if they are heavier than 850 g.
(a)
A fish is randomly selected from the lake.
(i)
Find the probability that this fish is big.
(b)
(c)
(ii) Given that this fish is big, find the probability that it is heavier than 900 g.
[6]
Two fishes are randomly selected. Find the probability that they are both big.
[2]
100 fishes are randomly selected.
(i)
(ii)
Find the expected number of these fishes that are big.
Find the probability that more than 2 of these fishes are big.
[6]
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