How do you read the standard normal table in DSE M1?

Find the row for the first decimal place of z and the column for the second. The entry is A(z), the area under the curve between 0 and z. For example, row 1.9 and column 0.06 give A(1.96) = 0.4750.

How do I standardise a normal variable?

Subtract the mean and divide by the standard deviation: Z = (X − μ)/σ. The result tells you how many standard deviations the value lies from the mean.

How many decimal places should z have?

Two, because the table is indexed to two decimal places. For a reverse lookup, take the table entry closest to the required area.

How to Use the Standard Normal Table (DSE M1)

Standardise with Z = (X − μ) / σ, so that Z ~ N(0, 1). The standard normal table printed in the DSE M1 paper gives A(z) = P(0 ≤ Z ≤ z), the area between 0 and z. Every other probability is built from it with 0.5 and symmetry: P(Z > z) = 0.5 − A(z) and P(Z < z) = 0.5 + A(z) for z > 0.

Solve Standardisation and the Standard Normal Table questions with AI

P(−0.5 < Z < 1.5) from Example 1. The shaded region grows until its right edge reaches z = 1.5, where the area is 0.6247. Try it yourself →

Standard Normal Table: Rules

StandardisingZ = (X − μ) / σ, E(Z) = 0, Var(Z) = 1

Table valueA(z) = P(0 ≤ Z ≤ z)

Right tailP(Z > z) = 0.5 − A(z)

Left of a positive zP(Z < z) = 0.5 + A(z)

Either side of 0P(−a < Z < b) = A(a) + A(b)

Same side of 0P(a < Z < b) = A(b) − A(a)

Worked Examples — Standardisation and the Standard Normal Table

Example 1: A probability on both sides of the mean

Find P(−0.5 < Z < 1.5), where Z ~ N(0, 1).

The interval straddles 0, so add the two areas: A(0.5) + A(1.5)
From the table: A(0.5) = 0.1915, A(1.5) = 0.4332
0.1915 + 0.4332 = 0.6247

Answer: 0.6247

Example 2: Reverse lookup: finding z from a probability

Find z such that P(Z < z) = 0.9.

0.9 is more than 0.5, so z is positive and A(z) = 0.9 − 0.5 = 0.4
Search the body of the table for the value closest to 0.4000: A(1.28) = 0.3997

Answer: z ≈ 1.28

💡 Exam Traps & Secrets

⚠️ The table starts from 0, not from −∞The DSE table gives the area from 0 to z. Many online tables and calculators give the area to the left of z instead, which is larger by 0.5. Always sketch the curve and shade what you want.

⚠️ Negative z: use symmetryThe table lists only positive z. Since the curve is symmetric, A(−z) is the same area as A(z): P(−1.2 < Z < 0) = A(1.2).

✏️ Self-Test: Quick Interactive Practice

How to study: Click any question below to instantly load it on the coordinate grid and check your steps.

(Right tail)Find P(Z > 1.25) and shade the region on the standard normal curve.

(Same side of 0)Find P(0.4 < Z < 1.6).

(Reverse lookup)Find z such that P(Z > z) = 0.025.