Your Practice Set – Applications and Interpretation for IBDP Mathematics
4 . The random variable X is defined such that E ( X ) � 180 and Var ( X ) � 12 . A random sample of n observations is selected from the distribution of X . Let X be the mean of
the sample . It is given that the standard deviation of X is 1 3 .
( a ) By using the central limit theorem , find n .
[ 2 ]
Another random variable Y is defined such that E ( Y) � 160 and Var ( Y) � 48 . A new random sample of 216 observations is selected from the distribution of Y . Let Y be the mean of the new sample . It is given that X and Y are independent .
( b ) Find P ( 9 � X �Y
� 21 ).
[ 3 ]
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