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In the normal curve distribution, what percent of the data falls: within one standard deviation [Select] mean? square about the

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In the normal curve distribution, what percent of the data falls: within one standard deviation [Select] mean? square about the

In the normal curve distribution, what percent of the data falls:
within one standard deviation [Select]
mean?
square 
about the

Solution

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ZanderProfessional · Tutor for 6 years

Answer

### 68%

Explain

## Step 1: Understanding Standard Deviation and Normal Distribution<br />### The standard deviation ($\sigma$) measures the spread of data around the mean ($\mu$) in a normal distribution. A normal distribution is a bell-shaped curve where the data is symmetrically distributed around the mean.<br /><br />## Step 2: The Empirical Rule (68-95-99.7 Rule)<br />### The empirical rule states that in a normal distribution:<br />### * Approximately 68% of the data falls within one standard deviation of the mean ($\mu \pm \sigma$).<br />### * Approximately 95% of the data falls within two standard deviations of the mean ($\mu \pm 2\sigma$).<br />### * Approximately 99.7% of the data falls within three standard deviations of the mean ($\mu \pm 3\sigma$).<br /><br />## Step 3: Applying the Empirical Rule to the Question<br />### The question asks for the percentage of data within one standard deviation of the mean. According to the empirical rule, this is approximately 68%.
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