09. Probability & Statistical Distributions

Probability is defined as the likelihood of an event or outcome in a trial. Statistical distributions are classified into two categories - discrete and continuous.

Discrete Distributions

Binomial Distribution: Describes the possible number of times that a particular event will occur in a sequence of binary observations. It is used when a researcher is interested in the occurrence of an event, not in its magnitude.

Poisson Distribution: An appropriate model for count data over fixed boundaries (e.g. infant mortality counts, bacteria counts on plates).

Continuous Distributions

Normal Distribution: A symmetric, bell-shaped Gaussian distribution with a single peak corresponding to the mean, median, and mode. It is characterized by Mean (location) and Standard Deviation (width).

A data set satisfies nearly normal distribution properties if:

• Most data values are clustered near the mean.
• Data values are spread evenly around the mean (symmetric).
• Larger deviations become rare, creating tapering tails.
• Individual parameters result from a combination of multiple factors.

The 68-95-99.7 Rules for a Normal Distribution:

• About 68.3% of the data falls within 1 standard deviation of the mean.
• About 95.4% of the data falls within 2 standard deviations of the mean.
• About 99.7% of the data falls within 3 standard deviations of the mean.