Math Problem Statement

The standardized score is also known as the ________________. A standardized score of 2.5 represents: Group of answer choices

z-score; the percentage of scores between the mean and 2.5 standard deviations above or below the mean

x-score; the percentile below which 2.5% all observations in the dataset can be found

x-Score; the shape of the probability distribution when the data are not normally distributed

z-score; the number that tells us the level of dispersion of the data about the mean

Solution

The correct answer is:

z-score; the percentage of scores between the mean and 2.5 standard deviations above or below the mean.

A standardized score, also known as the z-score, measures how many standard deviations a data point is from the mean of the dataset. A z-score of 2.5 indicates that the value is 2.5 standard deviations above the mean. In a normal distribution, the area between the mean and a z-score of 2.5 represents a certain percentage of the data.

Would you like further clarification or more details on how z-scores relate to normal distributions?

Here are five related questions for deeper understanding:

  1. What is the formula for calculating a z-score?
  2. How is the area under the normal curve between two z-scores found?
  3. What percentage of data lies between the mean and a z-score of 1 in a standard normal distribution?
  4. How would you interpret a negative z-score?
  5. How do z-scores help in comparing data from different distributions?

Tip: A z-score allows you to compare values from different datasets by standardizing them to a common scale (the standard deviation).

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Math Problem Analysis

Mathematical Concepts

Statistics
Standardized Scores
Normal Distribution
Z-scores

Formulas

Z = (X - μ) / σ

Theorems

68-95-99.7 Rule (Empirical Rule)
Standard Normal Distribution

Suitable Grade Level

Grades 10-12