Apps. and Interpretation for IBDP Maths Ebook 2 | Page 353

Answers
Exercise 65
65.1
( a )
( i )
640 g
( ii )
256 g
( b )
( i )
760 g
( ii )
20.4 g
( c )
P ( Y �795 ) �
0.957
65.2
( a )
( i )
1068 cm
( ii )
54 cm
( b )
P ( 1070 � X �1090 ) �
0.391
( c ) P ( Y �330 ) � 0.995 65.3 ( a ) P ( X �Y �1000 ) � 0.0805
( b ) P ( X �Y
� 0 ) � 0.920
65.4
( a )
0.367
( b )
0.0368
Exercise 66
66.1 ( a ) E ( X �Y) � 9 ( b ) P ( 5 � X �Y
� 8 ) � 0.208 ( c ) Var ( X �4 Y) � 61.5
66.2 ( a ) E ( W � X �Y) � 34
( b ) P ( W � X �Y
� 30 ) � 0.776
( c ) Var ( 3W � 2 X �Y) � 184
66.3
( a )
39.5
( b )
0.0627
( c )
6.10�
10 �8
66.4
( a )
375
( b )
0.0205
( c ) 8.67 � 10 �6
67.3 ( a ) E ( X ) � 0.45 ( b ) Var ( X ) � 0.4365 ( c ) E ( �X �Y) � 0.75
( d ) Var ( �X
�Y) � 1.2365
67.4
( a )
( i )
1
5
( ii )
3 P ( X �0 )
�
5
( iii )
E ( X ) �
6
( b )
Chapter 16
Exercise 68
1
E ( Y) �
3
68.1
( a )
300
( b )
1 Var ( X
) �
40
( c ) P ( X � 299.85 ) � 0. 171
68.2
( a )
�
2
( b )
1
2
( c ) P ( X �1.5 ) � 0.159
68.3
( a )
5
( b )
4 Var ( X
) �
125
( c ) P ( X �Y
� 0.1 ) � 0.324
68.4 ( a ) n � 108 ( b ) P ( 9 � X �Y � 21 ) � 0.958
Exercise 67
67.1 ( a ) E ( X ) � 3.7 ( b ) E ( 5X
�2 Y) � 38.5 ( c ) Var ( 5X
�2 Y) � 140.75
67.2 ( a ) E ( X ) � 65 ( b ) Var ( X ) � 22.75 ( c ) E ( 2X
�7 Y) � � 80
( d ) Var ( 2X �7 Y) � 434
Exercise 69
69.1
( a )
sn �
1 �
5.09
( b )
59
69.2 ( a ) s � 1.2
2 n
( b )
195
69.3
( a )
sn �
2.35
( b )
�
228
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