Z-table Practice Visuals

Z-table Visual Practice

1. Shaded Normal Curve Templates

Use these visuals to connect the picture of the area with the table operation.

P(Z < z) – Left Tail

-3 -2 -1 0 1 2 3
z

Shaded area is the table value directly for left-tail questions.

Flow:
  1. Standardize to \( z = \frac{x - \mu}{\sigma} \).
  2. Draw curve and shade left of z.
  3. Read area from the table: this is \(P(Z < z)\).

P(Z > z) – Right Tail

-3 -2 -1 0 1 2 3
z

Shaded area is the right tail, but tables give left area → use complement.

Flow:
  1. Standardize to z.
  2. Draw curve and shade right of z.
  3. Look up table(z) = left area.
  4. Compute \(1 - \text{table(z)} = P(Z > z)\).

P(a < Z < b) – Middle

-3 -2 -1 0 1 2 3
a
b

Shaded area is the difference of two left areas.

Flow:
  1. Standardize both bounds: a, b.
  2. Draw and shade between a and b.
  3. Compute \(\text{table(b)} - \text{table(a)}\).

2. Symmetry Reminder

Use this idea to show that the graph is symmetric around 0.

You can duplicate the left/right-tail cards above with z and −z to emphasize this symmetry.

3. Self-Practice Questions (Click to Reveal)

Q1. A normal variable has mean 0, sd 1. Find \(P(Z < 1.0)\).

1) Sketch a bell curve, mark z = 1, and shade the left tail.

2) Decide: is this left, right, or between?

Type: Left tail. Table gives \(P(Z < 1.0) \approx 0.8413\). So the answer is about 0.84.

Q2. Find \(P(Z > 1.5)\).

1) Sketch, mark z = 1.5, shade the right tail.

2) Decide if you need table(z) or 1 − table(z).

Type: Right tail. Table gives \(P(Z < 1.5) \approx 0.9332\). So \(P(Z > 1.5) = 1 - 0.9332 \approx 0.0668\).

Q3. Find \(P(-0.5 < Z < 1.0)\).

1) Sketch, mark z = −0.5 and z = 1.0, shade the middle region.

2) Use the idea “difference of two left areas”.

Type: Between two z-values. Table(1.0) ≈ 0.8413, Table(−0.5) ≈ 0.3085. So area = 0.8413 − 0.3085 ≈ 0.5328.

You can clone these .question blocks and change z-values to create more drills. Ask her to first label the picture on paper, then click “Show Answer” to check her table work.