3 . In a snack shop , the weights of candy boxes are normally distributed with mean 500 g and standard deviation 13 g , and the weights of chocolate boxes are normally distributed with mean 470 g and standard deviation 17 g . Let X and Y be the weight of a candy box and a chocolate box respectively .
A candy box and a chocolate box are randomly chosen .
( a ) Find P ( X �Y
� 1000 ) .
( b ) Find the probability that the candy box is heavier than the chocolate box .
4 . In a town , the waiting times for buses are normally distributed with mean 10 minutes and standard deviation 1.5 minutes , and the waiting times for taxis are normally distributed with mean 7 minutes and standard deviation 0.75 minutes . Let X and Y be the waiting time for a bus and a taxi respectively , on a particular day .
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15
( a ) Find P ( 16.2 � X �Y
� 17.8 ).
( b ) Sam starts his journey on a particular day and he needs to take either a bus or a taxi . Find the probability that a bus arrives earlier than a taxi .
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