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Standard Normal Distribution definitions

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  • Standard Normal Distribution
    A symmetric, bell-shaped curve with a mean of zero and a standard deviation of one, used as a reference for probability calculations.
  • Z-Score
    A value representing the number of standard deviations a data point is from the mean on the standard normal curve.
  • Z-Table
    A chart listing cumulative probabilities for z-scores, allowing quick lookup of areas under the standard normal curve.
  • Cumulative Probability
    The total area under the curve to the left of a specific z-score, representing the probability up to that point.
  • Complement
    The probability of the area to the right of a z-score, found by subtracting the left area from one.
  • Continuous Random Variable
    A variable that can take any value within a range, with probabilities represented by areas under a curve.
  • Density Curve
    A graphical representation where the area under the curve corresponds to probability for a continuous variable.
  • Area to the Left
    The region under the standard normal curve from negative infinity up to a given z-score, matching cumulative probability.
  • Area to the Right
    The region under the standard normal curve from a given z-score to positive infinity, found using the complement.
  • Mean
    The central value of the standard normal distribution, always located at zero on the horizontal axis.
  • Standard Deviation
    The measure of spread in the standard normal distribution, with each z-score unit representing one increment.
  • Probability
    The likelihood of a value or range occurring, represented by the area under the standard normal curve.
  • Hypothesis Testing
    A statistical method using the standard normal distribution to assess evidence against a claim.
  • Interval
    A range between two z-scores, with its probability found by subtracting the smaller cumulative area from the larger.
  • Hundredths Place
    The second decimal position in a z-score, used to precisely locate values in the z-table.