MPC06 December 2022: Discuss the characteristics of normal probability curve. (Marks 6)

 

Discuss the characteristics of normal probability curve.                                      6

Ans: The characteristics of the normal probability curve are:

1)     The Normal Curve is Symmetrical: The normal probability curve is symmetrical about its vertical axis (the ordinate). This symmetry implies that the size, shape and slope of the curve on one side of the curve is identical to that of the other, as shown in the figure given here

2)     The Normal Curve is Unimodel: The curve has only one peak or maximum point, thus the normal probability curve is unimodel, i.e. it has only one mode.

3)     The Maximum Ordinate occurs at the Center: The maximum height of the ordinate always occur at the central point (mean) in the unit normal curve and it is equal to 0.3989.

4) The Normal Curve is Asymptotic to the X Axis: The normal probability curve approaches the horizontal axis asymptotically; i.e. the curve never touches the horizontal (X) axis. It extends indefinitely in both directions, from minus infinity (−∞) to plus infinity (+∞).

5)     The Height of the Curve declines Symmetrically: In the normal probability curve the height declines symmetrically in either direction from the maximum point. This symmetric decline reflects the balanced distribution of data around the mean.

6)     Points of Inflexion occur at point ±1 Standard Deviation (± 1 σ): The shape of the normal curve changes its direction from convex to concave at a point recognised as point of influx. If we draw the perpendiculars from these two points of influx of the curve to the horizontal X axis; touch at a distance one standard deviation unit from above and below the mean (the central point)

7)     The Total Percentage of Area of the Normal Curve within Two Points of Influxation is fixed: Approximately 68.26% of the total area under the normal curve lies between ±1 standard deviation from the mean.

8)     Total Area Represents 100% Probability: The total area under the normal curve is considered to represent 100 percent probability. The specified area under each unit of standard deviation are shown in this figure.

9)     The Normal Curve is Bilateral: Half of the area under the curve lies to the left side of the maximum central ordinate and half of the area lies to the right side. That is, 50% of the data are below the mean and 50% are above it. Hence the curve is bilateral.

10)     A mathematical model in behavioural Sciences Specially in Mental Measurement: This curve is used as a measurement scale. The measurement unit of this scale is ± 1σ (the unit standard deviation).