Let X be a normal random variable with mean 0 and variance 25, and let Z be a st

Question

Let X be a normal random variable with mean 0 and variance 25, and let Z be a standard normal random variable. Which expression in terms of Z is P(X 5) equal to?

P(Z -2)

P(Z -1)

P(Z 0)

P(Z 1)

P(Z 2)

Let X be a normal random variable with mean 1 and variance 4, and let Z be a standard normal random variable. Which expression in terms of Z is P(X 2) equal to?

P(Z -1)

P(Z -1/2)

P(Z 0)

P(Z 1/2)

P(Z 1)

P(Z -2)

P(Z -1)

P(Z 0)

P(Z 1)

P(Z 2)

Let X be a normal random variable with mean 1 and variance 4, and let Z be a standard normal random variable. Which expression in terms of Z is P(X 2) equal to?

P(Z -1)

P(Z -1/2)

P(Z 0)

P(Z 1/2)

P(Z 1)

Explanation / Answer

1) = 0

= sqrt(25) = 5

Z = (X - ) /

X = 5

Z = (5 - 0) / 5 = 1

P(X < 5) = P(Z < 1) (ans)

Option-D) P(Z < 1)

2) = 1

= sqrt(4) = 2

Z = (X - ) /

X = 2

Z = (2 - 1) / 2 = 0.5

P(X < 2) = P(Z < 0.5)

Option-D) P(Z < 1/2)

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