Let Y₁, Y₂, Y3, Y₁, Ys and X₁, X₂, X, be independent and normally distributed random samples from populations with means #₁ = 2 and ₂ = 8 and variances ₁²=5 and 0₂² = k₁ respectively. Suppose that P(X-Ỹ> 10) = 0.02275, find the value of ₂² = k.

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