It is
bell-shaped
and has a single peak at the
center of the distribution.
2.
It is
symmetrical
about the mean
3.
It is
asymptotic
:
The curve gets closer and
closer to the
X
-axis but never actually touches it.
4.
The location of a normal distribution is
determined by the mean,
μ
, the dispersion or
spread of the distribution is determined by the
standard deviation,
σ
.
5.
The arithmetic
mean
,
median, and mode are
equal
6.
The total
area under the curve is 1.00
; half the
area under the normal curve is to the right of this
center point and the other half to the left of it
Different Means and
Standard Deviations
Equal Means and
Different Standard
Deviations
Different Means and Equal Standard Deviations
Family of Distributions
LO3
List the characteristics of the
normal probability distribution.
7-5

The Standard Normal
Probability Distribution
n
The standard normal distribution is a
normal distribution with a mean of 0 and
a standard deviation of 1.
n
It is also called the
z
distribution.
n
A
z-
value
is the signed distance
between a selected value, designated
X
,
and the population mean
μ
, divided by
the population standard deviation,
σ
.
n
The formula is:
LO4
Convert a normal distribution to
the standard normal distribution
7-6

The Normal Distribution – Example
The weekly incomes of
shift foremen in the
glass industry follow the
normal probability
distribution with a
mean
of $1,000
and a
standard deviation of
$100
.
What is the
z
value
for
the income, let
’
s call it
X,
of a foreman who
earns
$1,100
per week?
For a foreman who
earns
$900
per week?
LO5
Find the probability that an observation on a normally
distributed random variable is between two values.
7-7

Normal Distribution – Finding Probabilities
EXAMPLE
The mean weekly income of a shift
foreman in the glass industry is
normally distributed with a mean of
$1,000 and a standard deviation of
$100.
What is the likelihood of selecting a
foreman whose weekly income is
between $1,000 and $1,100?

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- Fall '19