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+10 votes

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. $1$
asked in Probability by Veteran (67.6k points) | 1.6k views

3 Answers

+16 votes
Best answer

answer = option A

answered by Veteran (29.8k points)
selected by
open eyes, look what is given in the 1st image.
Well explained. Thanks :-)

why minus sign used in last line 


+12 votes
First lets convert both X and Y to Standard normal distribution.



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.

Answer is Option A
answered by Active (2.3k points)
+1 vote
(A) is the correct answer?
answered by (35 points)
yes it is.

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