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Finding Probabilities, Z Values, and X Values with the Normal Distribution-Excel definitions

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  • Standard Normal Distribution
    A probability model with mean zero and standard deviation one, used for z scores and Excel's norm.s.dist and norm.s.inv functions.
  • Normal Distribution
    A continuous probability model defined by any mean and standard deviation, used for general cases in Excel's norm.dist and norm.inv functions.
  • Z Score
    A standardized value indicating how many standard deviations a data point is from the mean, used in standard normal calculations.
  • X Value
    A raw data point in a normal distribution, converted to probabilities or found from probabilities using Excel functions.
  • Cumulative Probability
    The chance of a value being less than or equal to a specified point, always representing the left tail in Excel's normal functions.
  • Left Tail Probability
    The probability that a value is below a given threshold, required as input for Excel's normal distribution functions.
  • Right Tail Probability
    The probability that a value exceeds a specified threshold, found by subtracting left tail probability from one.
  • Complement Rule
    A principle stating that the probability of an event equals one minus the probability of its complement, used for tail conversions.
  • Mean
    The central value of a distribution, required as an input for Excel's norm.dist and norm.inv functions for general normal distributions.
  • Standard Deviation
    A measure of spread in a distribution, used as an input for Excel's normal functions to define variability.
  • NORM.S.DIST
    An Excel function calculating cumulative probabilities for z scores in the standard normal distribution.
  • NORM.DIST
    An Excel function calculating cumulative probabilities for x values in any normal distribution, requiring mean and standard deviation.
  • NORM.S.INV
    An Excel function converting left tail probabilities into z scores for the standard normal distribution.
  • NORM.INV
    An Excel function converting left tail probabilities into x values for general normal distributions, using mean and standard deviation.
  • Continuous Random Variable
    A variable that can take any value within a range, modeled by the normal distribution and analyzed using Excel's functions.