Apps. and Interpretation for IBDP Maths Ebook 1 | Page 337

Solution
(a) (i) r �� 0.9717142437
(A1) for correct value
r �� 0.972
A1 N2
(b)
(c)
(ii) a �� 0.0432
A1 N1
b � 9432
A1 N1
The estimated insurance cost
� �0.0432(25000) � 9432
(A1) for substitution
� 8352
(A1) for correct value
� $8400
A1 N3
The insurance cost
8
� 8352 �(1 � 3%)
(M1)(A1) for correct formula
8
�8352 � 0.97
(A1) for simplification
� 6545.824538
� $6550
A1 N4
t
(d) 8352 �(1 �3%) � 5000
(M1) for setting equation
t
8352 �0.97 �5000 � 0
(A1) for simplification
By considering the graph of
t
y � 8352 �0.97 � 5000 , t � 16.84427 . (A1) for correct value
Thus, the year is 2036. A1 N4
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Exercise 95
22
1. Yuto is a beekeeper who collected data about monthly honey production in his bee hives.
The data for five of his hives on 1 January 2018 is shown in the following table.
Number of bees ( x ) 490 620 750 815 830
Monthly honey production
( y kg)
1.3 1.5 1.7 2.2 2.8
The relationship between the variables is modelled by the regression line with equation
y �ax � b .
(a) (i) Find the correlation coefficient.
(ii) Write down the value of a and of b .
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