Normal Distribution Curve
PRESENTER: STUTI DEWAN
5482
Contents
‣ Definition
‣ Features of Normal Distribution curve
‣ Standard Normal Curve
‣ z -Score
‣ Examples
Definition
‣
It is a continuous probability distribution for a random variable
‣ It represents the distribution of data in a bell shaped curve in a large
sample
‣
It is also known as called Gaussian distribution, after the German
mathematician Carl Gauss who first described it.
‣
Example , if we collect the haemoglobin values of a very large number of
people and make a frequency distribution
Features of Normal distribution curve
1. The mean, median, and mode are equal. Coincide at the centre point
2. The normal curve is bell-shaped and is symmetric about the mean.
3. The normal curve approaches, but never touches, the x-axis as it extends
farther and farther away from the mean.
4. The total area under the normal curve is equal to 1 or 100%. (Means the
whole population is accounted for)
Empirical rule :
▸ Between -1 SD and +1 SD : 68% of
the population lies
▸ Between -2 SD and +2 SD : 95% of
the population lies
▸ Between -3 SD and +3 SD : 99.7% of
the population lies
These limits on either side of the mean are called "confidence
limits" and are as shown in Fig. 15.
Supposing we are considering the 95 % confidence limits
.When we say this, we mean that 95 % of the area of the
normal curve. Therefore, the probability of a reading falling
outside the 95 per cent confidence limits is 1 in 20 (P = 0.05).
Standard normal curve
‣
Although there is an infinite number of normal curves depending upon the
mean and standard deviation, there is only one standardized normal curve,
which has been devised by statisticians to estimate easily the area under
the normal curve, between any two ordinates
‣
The total area of the curve is 1 ; its mean is 0 ; and its standard
deviation is 1.
Z-score
‣
The distance of a value (x) from the mean (x) of the curve in units of
standard deviation is called "relative deviate or standard normal
variate" and is usually denoted by Z. (It is basically how many standard
deviations above or below the mean)
‣ The standard normal deviate or Z is given by the formula :
Example
‣ The mean pulse rate of a group of individuals is 72/min with standard deviation of
4/min. Assuming the pulse rate follows normal distribution, what is the percentage
and probability of population that will have pulse rate 76 and above?
Ans. Assuming that the population mean pulse rate follows normal distribution
Here we use standard normal curve concept to find out % and probability of
individuals having pulse rate 76 and above.
Standard normal deviation (z) =
•
Probability (z>1) = Half of area of curve - Probability (z<1)
= 0.5 - 0.3414
= 0.1586
P = 0.16
Therefore, 16% of the population has pulse rate 76 and above with a probability of
0.16
References
‣
Park's Textbook of Preventive and Social Medicine 26th edition
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