The normal distribution

Now that we know what probability mass and probability density functions are and we know how to calculate some summary statistics, let's consider the normal distribution. The normal distribution, als known as the Gaussian distribution, is the probability distribution that is encountered most frequently. It is characterized by a nice bell curve. A normal distribution is centered at its mean called \(\mu\). Its spread is defined by the standard deviation. The image below gives an idea how the probability density function and the standard deviation of a normal distribution are related:

Look at the visualization; what is the probability that an observation from a normal distribution is between 1 standard deviation below the mean and 2 standard deviations above the mean?

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This probability is 0.68
This probability is 0.95
This probability is 0.815
This probability is 0.61

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Exercise

The normal distribution

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