Transcript Normal distribution I

Construction Engineering 221
Probability and statistics
Normal Distribution
Normal distribution
• Normal distribution is continuous (X can
assume any value- measurement)
• Binomial was discrete distribution (X can
assume only certain values, usually
integer values representing counts)
• Binomial is the most common counting
distribution (probability)
• Normal distribution is the most common
measurement distribution (classification)
Normal distribution
• Normal distribution is described by two
parameters, mean μ and variance σ2
• The shape of the graph (distribution)
varies for each population or sample
based on the mean and variance, but each
normal distribution has the same equation
as noted on page 67 in the book
Normal distribution
• Normal distributions are symmetrical about
the mean, and the curves never intercept
the X-axis,
• Normal distribution describes a great
number of natural phenomena (height,
weight, intelligence, measurement errors
of materials, test scores) occurring in a
population
Normal distribution
• Standardization- set the mean to 0 and the
standard deviation to 1, a simple
transformation
• X-μ/σ is the standardization equation.
• Example ACT is a normalized test with a
mean of 18 and a sd of 6. If you scored
an 18, you would have a standardized
score of 0 (0-0/6) or the mean of a
standardized distribution
Normal distribution
• If you had a score of 30, you would have a
standardized score of 30-18/6, or 2,
meaning two standard deviations above
the mean.
• When variables are standardized in this
manner (an ACT score of 30 is
transformed to “2”), they are denoted by
the letter z
Normal distribution
• Using standardized (z) values allows for the
production of standard normal tables to define
areas under the curve (probabilities or
percentages)
• Need to keep track of 1-tail versus 2-tail
probabilities
• Can also calculate areas under the curve
between values
• Review normal distribution tables on page 180181- note the rule of 9’s and 5’s