Pregunta
Which of the following groups of terms can be used interchangeably when working with normal distributions? Choose the correct answer below. z-scores, probability, and relative frequencies areas, z-scores, and probability areas, probability, and relative frequencies areas, z-scores, and relative frequencies
Ask by Donnelly Guerrero. in the United States
Feb 28,2025
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The terms "areas," "probability," and "relative frequencies" can be used interchangeably when working with normal distributions.
Solución
The correct answer is: areas, probability, and relative frequencies.
Explanation:
When working with normal distributions, the area under the curve is interpreted as the probability of an event occurring. Similarly, when looking at large samples, these probabilities approximate the relative frequencies. Therefore, the terms "areas," "probability," and "relative frequencies" are used interchangeably. Z-scores, on the other hand, are standardized values that indicate how many standard deviations an observation is from the mean, and are not interchangeable with the other three terms.
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Did you know that the concept of z-scores was developed by statisticians in the early 20th century? A z-score represents the number of standard deviations a data point is from the mean, making it a powerful tool for understanding and comparing data within a normal distribution. In real-world applications, understanding areas under the curve of a normal distribution is crucial in fields like psychology and quality control. For instance, measuring test scores or product dimensions often involves determining probabilities and relative frequencies, allowing businesses and researchers to make informed decisions based on statistical data.
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