Let X 1 , , X n be an i i d sequence of normal random variables with mean and variance 2 Let S n X 1 X n (a) Suppose 5 and 2 1 Find P( X 1 ) (b) Suppose 5, 2 1, and n 9 Find P( S n n ) ...

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Let X 1 , . . . , X n be an i.i.d. sequence of normal random

Question:

Let X₁, . . . , X_n be an i.i.d. sequence of normal random variables with mean μ and variance σ². Let S_n= X₁+ · · · + X_n.
(a) Suppose μ = 5 and σ² = 1. Find P(|X₁ − μ| ≤ σ).
(b) Suppose μ = 5, σ² = 1, and n = 9. Find P(|S_n/n − μ| ≤ σ).