Question

If X is a normal random variable with u = 2 and σ^2 = 4, find P(X < -1), P(X > 0), and P(0 < X < 1).

Answer 1

X ~ N ( 2 , 4 )

Where = 2 and = sqrt ( 4) = 2

We convert this to standard normal as

P(X < x) = P(Z < (x - ) / )

a)

P(X < -1) = P(Z < (-1-2) / 2)

= P(Z < -1.5)

= 0.0668 ( From Z table)

b)

P(X > 0) = P(Z > ( 0 - 2) / 2)

= P(Z > -1)

= P(Z < 1)

= 0.8413 ( From Z table)

c)

P(0 < X < 1) = P(X < 1) - P(X < 0)

= P(Z < ( 1 - 2) / 2) - P(Z < ( 0 - 2) / 2)

= P(Z < -0.5) - P(Z < -1)

= 0.3085 - 0.1587 ( From Z table)

= 0.1498