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Unformatted text preview: culated the areas below the standard Normal density function with
di↵erent cuto↵s (way before the computer age...), and we can look up the probabilities from
the table. Remark. The following standard Normal distribution table (handout) gives the probability that
a standard normal random variable, Z , falls between the values of 0 and some z > 0, i.e.
P (0 < Z ≤ z ).
Example 3.1. Q: Suppose Z follows the standard Normal distribution, using the standard
normal distribution table to ﬁnd the probability that 0 < Z ≤ 1.96.
A:
standard normal pdf: fZ (x) 0 1.96 x • Step 0 (Identify the cuto↵ z ): z = 1.96;
• Step 1 (Locating the corresponding row by ﬁnding the ﬁrst two digits of z on the left
column): row = “1.9”;
• Step 2 (Locating the corresponding column by ﬁnding the last digit of z on the top row):
column = “0.06”;
• Step 3 (Read the probability o↵ the table): P (0 < Z ≤ 1.96) = 0.475. Example 3.2. Q: Suppose Z follows the standard...
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This document was uploaded on 03/27/2014 for the course MA 107 at Quinnipiac.
 Fall '13
 Alexandru
 Probability

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