Exam P normal table (z-table), with a lookup

Exam P gives you one table, the standard normal, on screen under the Exhibit button. Here it is, with a lookup that finds the probability or the z and shows where to read it.

From the table

0.9750

From exact z: 0.9750

How to read it

z = 1.96
P(Z < 1.96) = 0.9750

P(Z < z), the standard normal table

The first decimal of z is down the side, the second across the top. Tap a value to look it up.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
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2.6
2.7
2.8
2.9
3.0
3.1
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3.7
3.8
3.9

z for common probabilities

P(Z < z)	0.750	0.800	0.850	0.900	0.950	0.975	0.990	0.995
z	0.6745	0.8416	1.0364	1.2816	1.6449	1.9600	2.3263	2.5758

On the exam	On screen under Exhibit; you may not bring your own copy
What it gives	P(Z < z) for z from 0.00 to 3.99, to four decimals
Answer choices	Computed from exact normal values: pick the closest

How to read it

Standardize: z = (x − μ) ÷ σ, then round z to two decimals.
Find the first decimal down the side and the second across the top.
Above a value: P(Z > z) = 1 − P(Z < z).
A negative z: P(Z < −z) = 1 − P(Z < z), since the curve is symmetric.
Between two values: subtract the smaller table value from the larger.

Values worth knowing

z = 1.645 leaves 5% in the upper tail, 1.960 leaves 2.5% and 2.326 leaves 1%. The two-sided 95% range is the mean plus or minus 1.960 standard deviations.

Rounding and the answer choices

SOA's notes to the table say the answer choices are computed from exact normal values, so rounding z to the table can land slightly off them. Choose the closest answer. The lookup shows both the table reading and the exact value.

Try 2 questions

Question 1

The total weekly claim amount is normally distributed with mean 1,000 and standard deviation 200 dollars.

Calculate the probability that it is between 850 and 1,300 dollars.

Question 2

An insurer has a portfolio of claims. Each of 100 independent claims has mean 250 and standard deviation 80 dollars.

Using the normal approximation, calculate the probability that the total of the 100 claims exceeds 26,000.

Next step

Take the free diagnostic Try the continuous distributions lesson

SOA's Exam P table and notes

Questions people ask

Is a z-table given on Exam P?

Yes. A standard normal table is shown on screen under the Exhibit button, so you may not bring your own copy.

Should I interpolate in the Exam P normal table?

SOA's notes say the answer choices use exact normal values and that rounding to the table may give a slightly different answer. Round z to two decimals and choose the closest answer.

What z gives the 95th percentile?

1.645, since P(Z < 1.645) = 0.95. For a two-sided 95% range, use 1.960.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0
0.1
0.2
0.3
0.4
0.5
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0.9
1.0
1.1
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1.6
1.7
1.8
1.9
2.0
2.1
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2.5
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2.7
2.8
2.9
3.0
3.1
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3.3
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3.5
3.6
3.7
3.8
3.9

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9