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Let X denote the wing length in millimeters of a male gallinule and Y the wing...

Let X denote the wing length in millimeters of a male gallinule and Y the wing length in millimeters of a female gallinule. Assume that X is N(184.09,39.37) and Y is N(171.93, 48.88) and that X and Y are independent. If a male and a female gallinule are captured, what is the probability that X is greater than Y?  

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Answer:

Given that:

Let X denote the wing length in millimeters of a male gallinule and Y the wing length in millimeters of a female gallinule. Assume that X is N(184.09,39.37) and Y is N(171.93, 48.88)

Since X and Y are normally distributed independent variables,the W=X-Y has the normal distribution

Thus using the table of normal distribution

  

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