Download 15.3 The normal Distribution

15.3 THE NORMAL DISTRIBUTION
Learn to recognize and analyze normal
distributions
BELL-SHAPED CURVES

data is clumped in the middle and tapered off at the extremes
Other examples:
heights of all 11th grade girls in a large city
 levels of soil samples from all farms in a rural county
 achievement test scores for all high school students in a state

STANDARD NORMAL DISTRIBUTION


mean = 0
standard deviation = 1
The Normal Distribution has:
• mean = median = mode
• symmetry about the center
• 50% of values less than the mean
and 50% greater than the mean
The spread of a normal
distribution is controlled
by the standard deviation; the
smaller the standard deviation
the more concentrated the data.
STANDARD NORMAL CURVE

bell-shaped curve that represents the standard normal
distribution
properties of the standard normal curve
1.
symmetric with respect to the y-axis
2.
approaches the x-axis asymptotically as |x| increases
3.
total area under the curve and above the x-axis =1
AREA UNDER THE STANDARD NORMAL CURVE
can be used to estimate the fraction of data
falling between two values
 tables have been developed to help find this area

AREA UNDER THE STANDARD
NORMAL CURVE FOR 0  x  4.0
IN A STANDARD NORMAL DISTRIBUTION…




what fraction of the data
is between 2.6 and 2.8?
what percent of data is
within two standard deviations from the mean?
what fraction of the data is more than 2.0?
what percent of the data is more than two
standard deviations from the mean?
STANDARDIZED VALUE CORRESPONDING TO Z
gives number of standard
deviations that “x” is from
the mean of the distribution
z
x

The heights of a certain group of adults are
normally distributed with a mean of 180 cm and a
standard deviation of 8cm.
Find the percent of the group having….
a. a height greater than 196 cm
b.
heights between 172 and 180