normal distribution curve

2. WHAT IS A BELL CURVE OR NORMAL CURVE?
• IN STATISTICS, THE THEORETICAL CURVE THAT SHOWS OFTEN AN EXPERI
MENT WILL PRODUCE APARTICULAR RESULT. THE CURVE IS SYMMETRICAL
ANDBELL SHAPED, SHOWING THAT TRIALS WILL USUALLY GIVEA RESULT N
EAR THE AVERAGE, BUT WILL OCCASIONALLY
DEVIATE BY LARGE AMOUNTS. THE WIDTH OF THE“BELL” INDICATES HOW
MUCH CONFIDENCE ONE CAN HAVE IN THE RESULT OF AN EXPERIMENT —
THE
NARROWER THE BELL, THE HIGHER THE CONFIDENCE.THIS CURVE IS ALSO
CALLED THE GAUSSIAN CURVE.

3. The Normal Distribution:
The Normal curve is a mathematical abstraction which
describes ("models") many frequency distributions of
scores in real-life.
All normal distributions are symmetric and have bell-
shaped d2ensity curves with a single peak.

4. CHARACTERISTICS OF A NORMAL/BELL SHAPE
CURVE
1. It is bell-shaped and asymptotic at the extremes.
Which means the
curve and the line do
not intersect each
other.

5. 2. It's symmetrical around the mean.
This means that the
mean (average) is always
in the center of the
curve and equal from
both sides

6. 3.The mean, Median and mode fall at
the middle point and they are
numerically equal.

7. 4. It can be specified completely, once mean
and SD are known.
5. The area under the curve is directly proportional
to the relative frequency of observations.

8. Bell Curve Standard Deviations
All normal density curves satisfy
the following property which is
often referred to as the Empirical
Rule.
68%of the observations fall within 1
standard deviation of the mean, that
is, between and .95%of the
observations fall within 2 standard
deviations of the mean, that is,
between and .99.7%of the
observations fall within 3 standard
deviations of the mean, that is,
between and .
Thus, for a normal distribution, almost all
values lie within 3 standard deviations of
the mean.

9. Advantages of the normal distribution
• The normal distribution is widely used partly because it does
genuinely often occur.
• It is also often used even when it just a rough approximation
because it is easy to handle.
• The normal distribution can be manipulated algebraically much
more easily than alternatives, so it can be used to derive
formulae. This means that it is possible to derive results that can
easily be applied (although computers have made this less
important).
• Academics also like to derive formulae (or “closed form
solutions”) for their own sake.

10. Problems and limitations
A number of valuation and risk models assume that the future
price of a security is normally distributed.
This is clearly false as a normal distribution function has a
positive value for any value of the future price, whereas the
price of a security cannot fall below zero.
A particularly important weakness, in the context of risk
models, is that real distributions are fat-tailed.
Their extremes are more probable than those of the standard
distribution, because of the risk of crashes and booms.
The normal distribution is easy to use and the assumption
that prices are normally distributed is sufficiently accurate in
many circumstances.