August 2011
Intermediate to advanced
634 pages
21h 57m
English
Content preview from A First Course in Quality Engineering, 2nd Edition
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104 A First Course in Quality Engineering
distribution� First, we will solve some examples to see how the standard normal
table is used to nd areas under the standard normal distribution�
Example 2.30
If Z ∼ N(0, 1):
a. Find P(Z ≤ 2.62).
b. Find P(Z ≤ −1.45).
c. Find P(Z > 1.45).
d. Find P(−1.5 ≤ Z ≤ 2.5).
e. Find t such that P(Z < t) = 0.0281.
f. Find s such that P(Z > s) = 0.0771.
g. Find k such that P(−k ≤ Z ≤ k) = 0.9973.
Solution
Sketches in Figures 2.13a to 2.13g have been made to help identify the areas under
the standard normal curve.
a. From the normal table, P(Z ≤ 2.62) = Φ(2.62) = 0.9956.
b. From the normal table, P(Z ≤ −
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