Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 65
1 . In a supermarket , the weights of apples are normally distributed with mean 160 g and standard deviation 8 g , and the weights of oranges are normally distributed with mean 220 g and standard deviation 12 g . Four apples are randomly chosen . Let X be the total weight of the selected apples .
( a ) Write down
( i ) the mean of X ;
( ii ) the variance of X .
Two apples and two oranges are randomly chosen . Let Y be the total weight of the selected fruits .
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( b ) Write down
( i ) the mean of Y ;
( ii ) the standard deviation of Y .
( c ) Hence , find P ( Y � 795 ) .
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2 . In a tutorial class , the male students ’ heights are normally distributed with mean 178 cm and standard deviation 3 cm , and the female students ’ heights are normally distributed with mean 165 cm and standard deviation 4 cm . Six male students are randomly chosen . Let X be the total height of the selected students .
( a ) Write down
( i ) the exact value of the mean of X ;
( ii ) the variance of X .
( b ) Hence , find P ( 1070 � X � 1090 ).
One male student and one female student are randomly chosen . Let Y be the total height of the two selected students .
( c ) Find P ( Y � 330 ) .
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