Download Day of birth relative to due date Day of birth relative to due date

STAT1010 – Normal Distribution intro
5.1 The Normal Distribution
  Many
variables tend to be distributed as a
normal distribution:
 Weights,
heights, IQ scores, etc.
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Day of birth relative to due date
This is a histogram
for a distribution of
300 natural births.
The left vertical axis
shows the number of
births for each 4-day
bin (as a count). The
right vertical axis
shows relative
frequencies.
Relative frequency
Due Date
(base line as 0)
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Day of birth relative to due date
The shape looks like
a normal distribution:
one peak
symmetric
‘bell-shaped’
Due Date
(base line as 0)
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STAT1010 – Normal Distribution intro
Day of birth relative to due date
Because this plot
shows relative
frequencies, we can
use it to determine the
probability that
babies are born at
certain times around
their due date.
Due Date
(base line as 0)
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Day of birth relative to due date
For instance, if we
consider all the bars
to the left of -14, add
their respective
relative frequencies,
we get 0.21. This
means, 21% of the
babies are born more
than 2 weeks (14
days) before their due
date.
Due Date
(base line as 0)
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Day of birth relative to due date
Because the bar
heights show relative
frequencies (right
vertical axis), when
the are all added up,
they MUST equal 1.
Due Date
(base line as 0)
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STAT1010 – Normal Distribution intro
Day of birth relative to due date
Here, we overlay the
observed data with a
theoretical normal
distribution curve.
The area under the
red curve is 1 or
100%.
The area under the
curve to the left of
-14 is 0.21 or 21%.
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Day of birth relative to due date
The area under the
curve to the left of
-28 is about 0.03 or
3%.
Only about 3% of the
babies are born more
than 4 weeks early.
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Normal Distribution
  There
are an infinite number of possible
normal distributions. They can each have
their own mean (center) and standard
deviation (spread).
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STAT1010 – Normal Distribution intro
Normal Distribution
  Definition:
The normal distribution is a symmetric,
bell-shaped distribution with a single peak.
Its peak corresponds to the mean, median,
and mode of the distribution. Its variation
can be characterized by the standard
deviation of the distribution.
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The Normal Distribution and
Relative Frequencies
  The
area that lies under the normal
distribution curve corresponding to a range
of values on the horizontal axis is the
relative frequency of those values.
  Because
the total relative frequency must
be 1, the total area under the normal
distribution curve must equal 1, or 100%.
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