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🎲intro to statistics review

Standard Normal Table

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The standard normal table, also known as the z-table, is a statistical tool that provides the probabilities or areas under the standard normal distribution curve. It is a crucial resource for solving problems involving normal distributions and standardized scores (z-scores).

5 Must Know Facts For Your Next Test

  1. The standard normal table provides the cumulative probabilities or areas under the standard normal curve for different z-scores.
  2. The table is used to find the probability of a value occurring within a certain range of the standard normal distribution.
  3. The table is symmetrical around the mean (0), so the probabilities for positive and negative z-scores are the same.
  4. The table is often used to convert raw scores into standardized z-scores, which allows for easier comparison and interpretation of data.
  5. The standard normal table is a crucial tool in hypothesis testing, confidence interval calculations, and other statistical analyses involving normal distributions.

Review Questions

  • Explain how the standard normal table is used to find the probability of a value occurring within a certain range of the standard normal distribution.
    • The standard normal table provides the cumulative probabilities or areas under the standard normal curve for different z-scores. To find the probability of a value occurring within a certain range, you first need to convert the raw score into a z-score using the formula: z = (x - μ) / σ, where x is the raw score, μ is the mean, and σ is the standard deviation. Once you have the z-score, you can use the standard normal table to look up the corresponding probability or area under the curve. The table gives the probability of a value being less than or equal to the given z-score, which can then be used to calculate the probability of the value falling within the desired range.
  • Describe how the standard normal table is used in hypothesis testing and confidence interval calculations.
    • In hypothesis testing, the standard normal table is used to determine the critical values or p-values associated with a test statistic (such as a z-score) under the null hypothesis. This allows researchers to assess the statistical significance of their findings and make decisions about rejecting or failing to reject the null hypothesis. Similarly, in confidence interval calculations, the standard normal table is used to find the z-score corresponding to the desired level of confidence (e.g., 95% or 99%), which is then used to calculate the upper and lower bounds of the confidence interval. The standard normal table is a crucial tool in these statistical analyses, as it provides the probabilities needed to make informed decisions and draw valid conclusions from the data.
  • Explain the importance of the standard normal table's symmetry around the mean (0) and how this property can be leveraged in statistical analyses.
    • The standard normal table is symmetrical around the mean (0), meaning that the probabilities for positive and negative z-scores are the same. This property can be leveraged in various statistical analyses. For example, when working with a standard normal distribution, you only need to look up the probability for a positive z-score, as the probability for the corresponding negative z-score will be the same. This symmetry also allows for simplification in calculations, as the probability of a value falling below a certain z-score is equal to 1 minus the probability of a value falling above that z-score. This symmetry is a fundamental characteristic of the standard normal distribution and the standard normal table, and understanding it can greatly streamline statistical problem-solving.