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Paper 1 – Problems Involving Normal Distribution
Example
In a school , the male students ’ weights are normally distributed with mean 60 kg and standard deviation 3 kg , and the female students ’ weights are normally distributed with mean 50 kg and standard deviation 3.5 kg . Three male students are randomly chosen . Let
X be the total weight of the selected students .
( a ) Write down
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( i ) the mean of X ;
( ii ) the variance of X .
One male student and two female students are randomly chosen . Let Y be the total weight of the selected students .
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( b ) Write down
( i ) the mean of Y ;
( ii ) the standard deviation of Y .
( c ) Hence , find P ( Y � 170 ).
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Solution
( a ) ( i ) 180 kg A1
( ii ) 27 kg A1
( b ) ( i ) 160 kg A1
( ii ) 5.79 kg A1
( c ) Y ~ N ( 160 , 33.5 ) P ( Y �170 ) � 0.0420176687
( A1 ) for correct value
P ( Y �170 ) � 0.0420 A1
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