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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 symmetric, bell-shaped curve with mean zero and standard deviation one, used for standardized z-scores.
  • Z-Score
    A standardized value indicating how many standard deviations a data point is from the mean.
  • Cumulative Probability
    The likelihood that a variable is less than or equal to a specific value, represented by the area under the curve to the left.
  • Left Tail Probability
    The probability that a value falls below a specified point in a distribution.
  • Right Tail Probability
    The probability that a value exceeds a specified point in a distribution.
  • Complement Rule
    A method for finding the probability of an event by subtracting the probability of its complement from one.
  • Population Mean
    The average value of all observations in a population, often denoted as mu.
  • Population Standard Deviation
    A measure of the spread of values in a population, denoted as sigma.
  • Normal Distribution
    A continuous, symmetric probability distribution defined by its mean and standard deviation.
  • X Value
    A specific data point or observed value within a normal distribution.
  • NORM.S.DIST
    An Excel function that returns the cumulative probability for a given z-score in the standard normal distribution.
  • NORM.DIST
    An Excel function that returns the cumulative probability for a given x value, mean, and standard deviation.
  • NORM.S.INV
    An Excel function that returns the z-score corresponding to a given cumulative probability in the standard normal distribution.
  • NORM.INV
    An Excel function that returns the x value corresponding to a given cumulative probability, mean, and standard deviation.
  • 68–95–99.7 Rule
    A guideline stating that about 68%, 95%, and 99.7% of data in a normal distribution fall within one, two, and three standard deviations from the mean.