Mathematics · Probability Theory

Let X and Y be independent random variables with X ~ N(2, 4) and Y ~ N(-4, 9). Given φ(1) = 0.8413, φ(2) = 0.9772, and φ(3) = 0.9987, where φ(·) is the CDF of a standard normal distribution. Which of the following statements is true?

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Correct answer

P(|2X + Y| ≤ 15) = 0.9974

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Let X and Y be independent random variables with X ~ N(2, 4) and Y ~ N(-4, 9). Given &phi;(1) = 0.8413, &phi;(2) = 0.9772, and &phi;(3) = 0.9987, where &phi;(&middot;) is the CDF of a standard normal distribution. Which of the following statements is true?