Multiple choice

Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X ≤ -1) = P (Y ≥ 2)$ , the standard deviation of $Y$ is

  1. 3

  2. 2
  3. $\sqrt{2}$

  4. 1
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A Correct answer
Explanation

X (1,4),4(-1,$\sigma^2$) P(x $\le$-1) Z = $\dfrac{-1-1}{2}$ = -1 = P (Z $\le$ -1) = P (Z $\ge$1) = 0.5 - P (0<z<1) = 0.1587 If $\sigma$= 3 then P(Z $\ge$ 2), Z = $\dfrac{2+1}{3}$= 1 = P (Z $\ge$1) = 0.1587

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