Question

Z us a standard normal random variable. What is the value of Z if between -Z and Z is .754?

Answer 1

Depending on how your table reports the probabilities, it may be easier to look at how much probability there is in the tails. 1-.754 = .246tells us that in both tails there is a total of .246 probability. since there are two tails you divide .246 by two and get .123. In your ztable, look up the z-score that will give you probability of .123 to the right of the z value.

To the right of 1.1 is probability .123. So we know that Z must be between -1.1 and 1.1

z=1.1

Answer 2

The area (probability) to right of z=1.16 is 0.123. P( z > 1.16) = .123

The area (probability) to left of z=-1.16 is 0.123 P( z < -1.16) = .123

So the area between z=-1.16 and z=1.16 is 1-2*.123 = 0.754

Depending on how your table reports the probabilities, when you go to row 1.1 and coloumn .06, you see either .877 or .123.

If it lists .877, then you know all the area to left of z=1.16, so because the total area is 1, you know the area to the right of z=1.16 is 0.123

And because the normal curve is symmetric, the area to the right of z=1.16, P( z > 1.16) is the same as the area to left of z=-1.16, P(z < -1.16)