Statisticians and mathematicians use the term "normal distribution" for this distribution, physicist

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Statisticians and mathematicians use the term
"normal distribution" for this distribution,
physicists sometimes call it a Gaussian
distribution and, because of its curved flaring
shape, social scientists refer to it as the "bell
curve."
X N(m,s2)
Normal distributions have many convenient
properties, so random variables with unknown
distributions are often assumed to be normal,
especially in physics and astronomy. Although
this can be a dangerous assumption, it is often a
good approximation due to a surprising result
known as the central limit theorem.
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The weight of a gallon container of milk is
approximately normally distributed with a mean of
8.5 pounds and a standard deviation of 0.03
pounds. What is the probability that a randomly
selected gallon of milk weighs less than 8.46
pounds?
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using EXCEL NORMDIST(8.46,8.5,0.03,TRUE)
m
x
s
X N(8.5, 0.032) P(X lt 8.46) 0.091
Normal CDF
Note Some calculators can do this also. (read
your instruction manual, look it up online, use a
magic 8-ball, etc.)
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Standard Normal
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The weight of a gallon container of milk is
approximately normally distributed with a mean of
8.5 pounds and a standard deviation of 0.03
pounds. What is the probability that a randomly
selected gallon of milk weighs less than 8.46
pounds?
Flip to pages 751 752 in your book
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Table A.3. Areas under the Normal Curve
P(Z lt -1.33) 0.0918
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Problem Types

• P(X lt 8.46) ?
• b. P(X gt 8.58) ?
• c. P(8.46 lt X lt 8.58) ?
• d. P(X lt 8.46 or X gt 8.58) ?

e. P(X lt x) 0.85 f. P(X gt x) 0.35 g. P(x lt
X lt 8.58) 0.15 h. P(8.46 lt X lt x) 0.30 i.
P(X lt x or X gt 8.58) 0.20 j. P(X lt 8.46 or X gt
x) 0.20
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Pages 185 187 Problems 6.1 6.22