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Statistics LibreTexts

6: Continuous Probability Distributions

  • Page ID
    5198
  • Chapter 5 dealt with probability distributions arising from discrete random variables. Mostly that chapter focused on the binomial experiment. There are many other experiments from discrete random variables that exist but are not covered in this book. This chapter deals with probability distributions that arise from continuous random variables. The focus of this chapter is a distribution known as the normal distribution, though realize that there are many other distributions that exist. A few others are examined in future chapters.

    • 6.1: Uniform Distribution
      If you have a situation where the probability is always the same, then this is known as a uniform distribution.
    • 6.2: Graphs of the Normal Distribution
      Many real life problems produce a histogram that is a symmetric, unimodal, and bellshaped continuous probability distribution.
    • 6.3: Finding Probabilities for the Normal Distribution
      The Empirical Rule is just an approximation and only works for certain values. What if you want to find the probability for x values that are not integer multiples of the standard deviation? The probability is the area under the curve. To find areas under the curve, you need calculus. Before technology, you needed to convert every x value to a standardized number, called the z-score or z-value or simply just z. The z-score is a measure of how many standard deviations an x value is from the mean.
    • 6.4: Assessing Normality
      The distributions you have seen up to this point have been assumed to be normally distributed, but how do you determine if it is normally distributed.
    • 6.5: Sampling Distribution and the Central Limit Theorem