# 3.2 Finding Percentiles Using the Standard Normal Table (for tables that give the area to left of z)

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Rate This Video Tags For This Video I work through some examples of finding the z value corresponding to a given area under the standard normal curve, using the standard normal table.

If you fully understand how to find values in the standard normal table, this video will not be of much use to you.

The table used is one that gives areas to the left of z (the cumulative distribution function).

### 2 Responses to “3.2 Finding Percentiles Using the Standard Normal Table (for tables that give the area to left of z)”

1. Sanchit Agarwal says:

Hello Sir.
I read about the Empirical rule and so straight after reading the question at 3:52, I evaluated the value of z0 to be 2, as a Standard Normal Distribution has SD=1, and the P(-z0<Z<z0)=.95 tells that z0=2SD = 2. But as you showed it in the table, it's 1.96 (slightly less than 2)..How's it different? Am I doing something wrong here?
Pls. suggest.. Thank you Sanchit Agarwa

• JB says:

The empirical rule is based on the normal distribution, but it’s just a rough guideline. In the empirical rule, we say that (for mound-shaped distributions) approximately 95% of the observations lie within 2 standard deviations of the mean. If we integrate the standard normal curve, we find that P(-1.96 < Z < 1.96) = 0.95. The empirical rule is just a rough guideline, so we use round numbers. Rather than say “approximately 95% of the observations lie within 1.96 standard deviations of the mean”, we go with 2.