Sampling Distribution of a Linear Combination of Means (3 of 4)

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Or, symbolically, what is the probability that:

15?

The answer lies in the sampling distribution of .

Letting a₁ = -.5, a₂ = -.5, and a₃ = 1,

L = .

The mean and standard deviation of the sampling distribution of L for this example are:

μ_L = a₁ μ₁ + a₂ μ₂ + ... + a_k μ_k

= (-.5)(60) + (-.5)(68) + (1)(80) = 16

and