Page 165 - Statistics for Dummies

Chapter 9: The Normal Distribution

1. Go to the row that represents the first digit of your z-value and the
first digit after the decimal point.

2. Go to the column that represents the second digit after the decimal
point of your z-value.
3. Intersect the row and column.

This result represents p(Z < z), the probability that the random variable
Z is less than the number z (also known as the percentage of z-values
that are less than yours).
For example, suppose you want to find p(Z < 2.13). Using the Z-table, find the
row for 2.1 and the column for 0.03. Intersect that row and column to find the
probability: 0.9834. You find that p(Z < 2.13) = 0.9834.
Suppose you want to look for p(Z < –2.13). You find the row for –2.1 and the
column for 0.03. Intersect the row and column and you find 0.0166; that means
p(Z < –2.13) equals 0.0166. (This happens to be one minus the probability that
Z is less than 2.13 because p(Z < +2.13) equals 0.9834. That’s true because the 149
normal distribution is symmetric; more on that in the following section.)
Finding Probabilities for
a Normal Distribution
Here are the steps for finding a probability when X has any normal distribution:
1. Draw a picture of the distribution.
2. Translate the problem into one of the following: p(X < a), p(X > b), or
p(a < X < b). Shade in the area on your picture.
3. Standardize a (and/or b) to a z-score using the z-formula:
4. Look up the z-score on the Z-table (Table A-1 in the appendix) and
find its corresponding probability.
(See the section “Standardizing from X to Z” for more on the Z-table).
5a. If you need a “less-than” probability — that is, p(X < a) — you’re done.
5b. If you want a “greater-than” probability — that is, p(X > b) — take one
minus the result from Step 4.
5c. If you need a “between-two-values” probability — that is, p(a < X < b) —
do Steps 1–4 for b (the larger of the two values) and again for a (the
smaller of the two values), and subtract the results.

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