6: Continuous Probability Distribution

Statistics C1000: Introduction to Statistics · LibreTexts

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    From LibreTexts, under CC BY-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    • 6.1: Introduction to the Normal Distribution
      The normal distribution is a continuous, bell-shaped, symmetric curve used to model many natural phenomena, with most values clustering around the mean. It is defined by its mean and standard deviation. Z-scores convert values to a standard scale, allowing you to find areas or probabilities using a table or calculator.
    • 6.2: Finding Probabilities for the Normal Distribution
      To compute probabilities using the normal distribution, convert values to z-scores and use a table or calculator to find the area under the curve. This area represents the likelihood of a value occurring. You can also use it in reverse to find cut-off scores for given probabilities.
    • 6.3: The Central Limit Theorem
      The Central Limit Theorem states that the distribution of sample means approaches a normal shape as sample size increases, regardless of the population's distribution. This allows us to compute probabilities about sample means using z-scores. It’s widely used in confidence intervals and hypothesis testing in inferential statistics.
    • 6.4: Formulas for Chapter 6
      This section contains key formulas for Chapter 6, including those for finding cutoff scores, calculating z-scores for the normal distribution, and calculating z-scores for the distribution of sample means. These formulas help analyze data using the normal distribution and distribution of sample means.
    • 6.5: Chapter 6 - Key Terms and Symbols
      This section includes all the key terms and symbols used in Chapter 6, providing a reference for concepts related to the normal distribution, standard scores, and sampling distributions.

    This page titled 6: Continuous Probability Distribution was last modified on Fri, 23 May 2025 23:16:48 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Toros Berberyan, Tracy Nguyen, and Alfie Swan.