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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. $1$

selected
open eyes, look what is given in the 1st image.
First lets convert both X and Y to Standard normal distribution.

Z=X-1/2

Z=Y+1/σ

Now replace X and Y in P(X<=-1)=P(Y>=2) we get P(Z<=-1)=P(Z>=3/σ)

Since the Standard Normal Curve is symmetric about the mean( i.e, zero) -(-1)=3/σ⟹σ = 3.

+1 vote