Let Y₁, Y2, Y3, Y4, Ys and X₁, X2,...,X9 be independent and normally distributed random samples from populations with means ₁ = 2 and 2 = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of ₂² = k.

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