Floating geometric shape image
Floating floating geometric shape image

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Just Normal
Probability
Given three independent and identically distributed normal variables \( X, Y, Z \) each following a normal distribution \( N(12, 12) \), calculate the probability \( P[X - Y > Z] \). The answer should be in the form of \( \Phi(a) \) for some value \( a \). Determine the value of \( a \).