. 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, 50.88) 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

The probability that X is greater than Y is 0.5754.

Step-by-step explanation:

It is provided that,

It is also provided that X and Y are independent.

We need to compute the value of:

P (X > Y) = P (X - Y > 0)

Compute the mean and standard deviation of (X - Y) as follows:

Compute the the value of P (X > Y) as follows:

Thus, the probability that X is greater than Y is 0.5754.