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Male weight exceeds twice female weight

High school · ●●●○○ 50 pts

The weights

X

kg of male birds are normally distributed with mean

4.8

and standard deviation

0.2

. The weights

Y

kg of female birds are normally distributed with mean

2.7

and standard deviation

0.15

X

and

Y

are independent. Find the probability that the weight of a randomly chosen male bird is more than twice the weight of a randomly chosen female bird. Give your answer correct to four decimal places.