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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
  • a)
    3
  • b)
    2
  • c)
    √2
  • d)
    1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let X be a random variable following normal distribution with mean +1...
X(,4),4(−1,σ2)
P(X ≤ −1)
Z = −1 − 1 / 2 = −1
\( = P(Z \geq-1) = P(Z \geq 1) = 0.5 - P(0 = 0.5 − 0.3413 = 0.1587
If σ = 3 then
P(Z ≥ 2),Z = 2 + 13 = 1
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Most Upvoted Answer
Let X be a random variable following normal distribution with mean +1...
Solution:

Given, X ~ N(1, 4) and P(X ≤ -1) = P(Y ≥ 2)

We need to find the standard deviation of Y.

Step 1: Finding the Probability

P(X ≤ -1) can be rewritten as P(Z ≤ ( -1 - 1 ) / 2) where Z is the standard normal variable.

P(Z ≤ -1) = 0.1587 (using standard normal distribution table)

Now, P(Y ≥ 2) can be rewritten as P(Z ≥ (2 + 1) / σ) where σ is the standard deviation of Y.

P(Z ≥ 3 / σ) = 0.1587

Step 2: Solving for σ

Using standard normal distribution table, we can find the value of Z for P(Z ≥ 3 / σ) = 0.1587

Z = 1.0

Therefore, 3 / σ = 1.0

σ = 3 / 1.0 = 3

Hence, the standard deviation of Y is 3.

Answer: Option (a) 3
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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 isa)3b)2c)√2d)1Correct answer is option 'A'. Can you explain this answer?
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