a.
However, in our course, you do not need to interpolate, but rather choose one of the two values. In this case since the two closest tabulated probabilities, 0.9495 and 0.9505,
were equidistant from 0.95, we just took the average of the row/column values 1.64 and 1.65 to get 1.645. You would get credit in this course for using 1.64 or 1.65 or 1.645.
•
Typical General Normal Probability Problems:
Let
X
be a
N
(10, 25) random variable (r.v.), where the mean μ is 10 and the variance σ
2
is 25, and the standard deviation (s.d.) is 5. Find the following probabilities.
a.
Find Pr(
X
< 0.2). First, we need to transform the general normal r.v. to the standard normal r.v.
Z
by using
Z
= (
X
μ)/σ. After making this transformation, the problem
becomes
Pr(
X
< 0.2) = Pr((
X
 10)/5 < (0.2  10)/5) = Pr(
Z
< 1.96) = 0.025.
b.
Find Pr(
X
< 19.8). The transformation given in (a) leads to
Pr(
Z
< (19.8  10)/5) = Pr(
Z
<1.96) = 0.975.
c.
Pr(3.6 <
X
< 19.8) = Pr((3.6  10)/5 <
Z
< (19.810)/5) = Pr(1.28 <
Z
< 1.96)
= Pr(
Z
< 1.96)  Pr(
Z
<
1.28) = 0.975  Pr(
Z
>
1.28) = 0.975  (1 .8997) = 0.8747.
d.
Pr(
X
 10 < 8.225) = Pr((
X
 10)/5 < 8.225/5) = Pr(
Z
 < 1.645) =
Pr
(1.645 <
Z
< 1.645) = 0.90.
•
Typical General Normal Percentile Problems:
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 Spring '08
 Nail
 Normal Distribution, Probability theory, Weibull, Lapin

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