If the expert is right what is the probability that a

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Unformatted text preview: a mean of 190 pounds and a SD of 25 pounds. If the expert is right, what is the probability that a random sample of 50 persons will cause an overload? State the assumptions you make, show your computations, and sketch your answer in a graph. X i = weight of person i T = total weight of 50 people ⎡ 50 ⎤ 50 E[T ] = E ⎢∑ X i ⎥ = ∑ E[ X i ] = 50(190) = 9500 ⎣1 ⎦1 Var (T ) = 50Var ( X ) = 50(25) 2 ⇒ SD(T ) ≈ 176.78 10,000 − 9500 ⎞ ⎛ P(T > 10,000) = P⎜ Z > ⎟ ≈ P( Z > 2.83) = 1 − .9977 = .0023 176.78 ⎝ ...
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