Pregunta
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QuICK CHECK Check all of the situations that you would expect to be approximately normally distributed. \( \square \) the SAT scores of high school seniors \( \square \) the salaries for members of a professional football team the shoe sizes of 17-year-old males the at which a child loses his or her first tooth toner

Ask by Fitzgerald Peters. in the United States
Feb 21,2025

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The SAT scores of high school seniors are approximately normally distributed.

Solución

To determine if a situation is approximately normally distributed, we need to check if the data follows a bell-shaped curve with the majority of the data points clustering around the mean and tapering off gradually towards the extremes. Let's analyze each situation: 1. **The SAT scores of high school seniors**: SAT scores are typically considered to be approximately normally distributed. This is because the scores are standardized and follow a bell-shaped curve. 2. **The salaries for members of a professional football team**: Salaries for professional football players can vary widely, and it is unlikely that they would follow a normal distribution. The salaries are often skewed towards the higher end, with a few players earning significantly more than the rest. 3. **The shoe sizes of 17-year-old males**: Shoe sizes can vary widely among individuals, and it is unlikely that they would follow a normal distribution. Shoe sizes are often skewed towards the larger end, with a few individuals having larger or smaller shoe sizes. 4. **The age at which a child loses his or her first tooth**: The age at which a child loses their first tooth is a random event and can vary widely among individuals. It is unlikely that this event would follow a normal distribution. Therefore, the situations that you would expect to be approximately normally distributed are: - The SAT scores of high school seniors

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The Deep Dive

The SAT scores of high school seniors are generally expected to follow a normal distribution due to the large number of test-takers and the design of the exam, which aims to assess a broad range of academic abilities. This results in a bell-shaped curve where most students score near the average, with fewer students scoring very high or very low. On the other hand, the salaries for members of a professional football team are likely to be highly skewed. A small number of star players tend to earn significantly more than the average player, leading to a distribution that is not normal. This can create an interesting spectacle in salary comparisons, as the elite few can greatly impact the overall average.

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