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
3.8
(177 Votes)
Madelyn
Master ยท Tutor for 5 years
Answer
### within one standard deviation: 68%### within two standard deviations: 95%### within three standard deviations: 99.7%### above the mean: 50%### between the mean and one standard deviation below the mean: 34%
Explanation
## Step 1: One Standard Deviation from the Mean### 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.## Step 2: Two Standard Deviations from the Mean### The empirical rule states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.## Step 3: Three Standard Deviations from the Mean### The empirical rule states that approximately 99.7% of the data in a normal distribution falls within three standard deviations of the mean.## Step 4: Above the Mean### In a normal distribution, the data is symmetrically distributed around the mean. Therefore, 50% of the data falls above the mean.## Step 5: Between the Mean and One Standard Deviation Below the Mean### 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.