MBADM813:

Lesson 2: Distributions

Lesson 2 Summary

• A probability distribution is a chart or a graph that shows the different possible values of the variable of interest (e.g., age, income, salary, sales, inventory level, number of calls coming in a call center, etc.) and the probability of observing that particular value.
• Probability distributions are calculated from relative frequencies. In a probability distribution, the sum of all probabilities equals 1.
  • If the probability distribution is displayed as a bar graph or a solid graph (for continuous variables), the area under the curve represents the possibility of observing all outcomes and thus equals 1.
  • The area on the left-hand side of a line, drawn vertically through the probability distribution, represents the probability of observing all outcomes up to the point, $P\left(X\le \dots \right)$ where the line is drawn.
  • The area on the right-hand side of a line, drawn vertically through the probability distribution, represents the probability of observing all outcomes beyond the point, $P\left(X\ge \dots \right)$ , where the line is drawn$.$$$
  • $P$$\left(X\ge \dots \right)=1-P\left(X\le \dots \right)<\dots )$$$
• The normal distribution is a continuous probability distribution. Many variables in our daily and business lives roughly follow the normal distribution. Examples may include, but are not limited to height, weight, IQ, call durations (for one specific type of call) at a call center, height/weight/width/length (i.e., the specification parameters) of a product in a production line, number of chips in a bag, the time taken for a routine doctor visit, and so on.
  • Although normal distributions are quite frequent, we often make a severe mistake in inference when we apply normal distribution formulas in scenarios where the underlying variable is not normally distributed. To avoid this mistake, look for
    • small sample size,
    • non-random sample, and
    • infrequent large spikes.
• Template to calculate probabilities and variable values based on the normal and z-distributions.