The “bell” curve
As the number of observations of numerical data increase, they tend to form a bell-shaped curve called the normal distribution or Gaussian distribution.
Properties of the normal distribution
- Symmetrical around the mean
- Continuous, so the probability is measured as the area under the curve
- Single mode
- Mean is the highest point
A standard normal curve has a mean of zero and a standard deviation of one
Z distribution and Z transformation
The Z distribution can be used to calculate probabilities using the standard normal distribution. It describes the probability that a random draw from the standard normal distribution is greater than a given value
A non-standard normal can be transformed to a standard normal using the Z transformation.
Law of large numbers
Law of large numbers: As you increase the sample size, mean and standard deviation remains the same, but standard errors become smaller.
Central limit theorem: the mean of a large random sample from any population is approximately normally distributed