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SOLUTION:

As X = 2Z + 1 we have 

(a) P(X < 0) = P(2Z + 1 < 0) = Φ(−1/2) = 1 − Φ(1/2) = 0.3085; 

(b) P(X > 1) = Φ(0) = 1/2; 

(c) P(−2 < X < 3) = Φ(1) − Φ(−3/2) = 0.7745; 

(d) P(|X + 1| < 1) = P(−2 < X < 0) = Φ(−1/2) − Φ(−3/2) = 0.2417.

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