Normal Probability Curve
A normal curve is a bell-shaped curve which shows the
probability distribution of a continuous random variable. Moreover, the normal
curve represents a normal distribution. The total area under the normal curve
logically represents the sum of all probabilities for a random variable. Hence, the area under the normal curve is
one. Also, the standard normal curve
represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal
distribution is mean ( μ ) and standard deviation ( σ ).
The
curve is symmetrical about a vertical line drawn through the mean, μ.
In theory, the mean is the same as the median, because the graph is symmetric
about μ. As the notation indicates, the normal distribution depends
only on the mean and the standard deviation. Since the area under the curve must equal one,
a change in the standard deviation, σ, causes a change in the shape of
the curve; the curve becomes fatter or skinnier depending on σ. A change in μ causes the graph to
shift to the left or right. This means
there are an infinite number of normal probability distributions. One of special interest is called the standard
normal distribution.
Characteristics Of Normal
Probability Curve
Major characteristics of normal probability
curve
Some of the main characteristics
of NPC are given below:
1. The curve is bilaterally
symmetrical.
The curve is symmetrical to its ordinate
of the central point of the curve. It
means the size, shape and slope of the curve on one side of the curve is
identical to the other side of the curve. If the curve is bisected then its right hand
side completely matches to the left hand side.
2. The curve is asymptotic. The Normal
Probability Curve approaches the horizontal axis and extends from-∞ to + ∞. Means the extreme ends of the curve tends to
touch the base line but never touch it.
3. The mean, median and mode. The mean, Median and
mode fall at the middle point and they are numerically equal.
4. The points of inflection occur at
± 1 standard deviation unit. The points of influx in a NPC occur at ± 1σ to
unit above and below the mean. Thus at
this point the curve changes from convex to concave in relation to the
horizontal axis.
5. The total area of npc is divided
in to ± standard deviations. The total of NPC is divided into six standard
deviation units. From the center it is
divided in to three +ve’ standard deviation units and three —ve’ standard
deviation units.
Thus
± 3σ of NPC include different number of cases separately. Between ± 1σ lie the middle 2/3rd cases or
68.26%, between ± 2σ lie 95.44% cases and between ± 3σ lie 99.73% cases and
beyond + 3σ only 0.37% cases fall.
6. The y ordinate represents the
height of the normal probability curve. The Y ordinate of the
NPC represents the height of the curve. At the center the maximum ordinate occurs. The height of the curve at the mean or mid
point is denoted as Y0.
7. It is unimodal. The curve is having
only one peak point. Because the maximum
frequency occurs only at one point.
8. The height of the curve
symmetrically declines. The height of the curve decline to both the
direction symmetrically from the central point. Means the M + σ and M — σ are equal if the
distance from the mean is equal.
9. The mean of npc is µ and the
standard deviation is σ. As the mean of the NPC represent the
population mean so it is represented by the µ (Meu). The standard deviation of the curve is
represented by the Greek Letter, σ.
10. The model ordinate varies
increasingly to the standard deviation. In a Normal
Probability curve the modal ordinate varies increasingly to the standard
deviation. The standard deviation of the
Normal Probability Curve increases, the modal ordinate decreases and
vice-versa.
Figure
1. Normal Curve
Table 1. Merits and Demerits of NPC
MERITS DEMERITS
Accurate for large class Not
good for small classes
More than 200 students Less
than 100 students
Healthy Unhealthy
POWER POINT PRESENTATION OF NPC
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