Page 54 - Math SL HB Sem 3

Normal Distribution

- a symmetrical continuous probability distribution

lf you measure a continuous quantity, like the height of a person, of a large population, it is likely
that the maiority of people are around the mean and fewer will be very tall or very short. The probability
distribution of such a case looks like:

(x)
f -------> Frequency

Rondom varioble
e.g. height

x
p --------> mean

This type of continuous probability distribution is called the normal distribution. We may express a
random variable X that is normally distributed as:
'-'can be read as'(X) is
X-N (p,o2) distributed as'

where lr the mean of the distribution
=
o the standard deviation of the distribution
=
az = the variance of the distribution

Characteristics of a normal distribution:

1) Bell-shaped

2) Symmetric about the mean

3) Mean = median = mode

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