Section B ( 41 marks )
7 . Five metal ingots were chosen at random and measurements were made of their breaking strength s and their hardness h . The results are shown in the table below .
Breaking strength ( s tonnes per cm ) 5 5.5 6 6.5 7 Hardness ( h ) 60 68 71 70 73
The relationship between the variables can be modelled by the regression equation h �as � b.
( a ) Write down the value of a and of b . [ 2 ]
( b ) Use the regression equation to estimate the hardness of a metal ingot when its breaking strength is 6.3 tonnes per cm .
[ 2 ]
There are 120 metal ingots in total . The cumulative frequency below shows the distribution of the hardness of all metal ingots .
Hardness less than |
Cumulative Frequency |
55 |
0 |
60 30
75 108
80 120
( c ) A metal ingot is randomly selected . Find the probability that the hardness of the selected ingot is
( i ) less than 75 ; ( ii ) at least 65 ; ( iii ) at least 75 , given that its hardness is at least 65 .
[ 6 ] Two metal ingots are randomly selected . The probability that the hardness of
the two selected ingots are both at least 70 is 29
476 .
( d ) Find q . [ 2 ]
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