Question
In the normal curve distribution, what percent of the data falls: within one standard deviation 68% about the mean? within two standard deviation [Select] square about the mean? within three standard deviation [Select] square about the mean? above the mean?[Select] square between the mean and one standard deviation square below the mean?
Solution
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MadelynMaster · Tutor for 5 years
Answer
### within one standard deviation: 68%<br />### within two standard deviations: 95%<br />### within three standard deviations: 99.7%<br />### above the mean: 50%<br />### between the mean and one standard deviation below the mean: 34%
Explain
## Step 1: One Standard Deviation from the Mean<br />### The empirical rule (or 68-95-99.7 rule) states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.<br /><br />## Step 2: Two Standard Deviations from the Mean<br />### The empirical rule states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.<br /><br />## Step 3: Three Standard Deviations from the Mean<br />### The empirical rule states that approximately 99.7% of the data in a normal distribution falls within three standard deviations of the mean.<br /><br />## Step 4: Above the Mean<br />### In a normal distribution, the data is symmetrically distributed around the mean. Therefore, 50% of the data falls above the mean.<br /><br />## Step 5: Between the Mean and One Standard Deviation Below the Mean<br />### Since 68% of the data falls within one standard deviation of the mean, and the distribution is symmetrical, half of this percentage (34%) falls between the mean and one standard deviation below the mean.
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