**Normal Distribution and Standard Deviation**

The normal distribution is a smooth, symmetric, continuous, bell shaped curve as shown. The distribution is neither skewed nor peaked. The spread of the normal distribution is characterized by the standard deviation.

What is the probability of obtaining a return exceeding or lower than the expected return?

In case of normally distributed returns, it depends only on the standard deviation. It is useful to notice certain properties of a normal distribution.

The distribution tabulated is a normal distribution with mean zero and standard deviation. Such a distribution is known as a standard normal distribution. However any normal distribution can be standardized and hence the table of normal probabilities will serve for any normal distribution.

**The formula to standardize is,**

S = (R – E (R))/ бR = Return which we are interested

S = (R – E (R))/ б

E (R) = Expected return

Б = Number of standard deviations from the expected return

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