A set of data is normally distributed with a mean of 500 and a standard deviation of 40. What percent of the data is between 460 and 540?
Answer: 68.3%
Yes, that is the definition of a standard deviation.
To find the percent of data between 460 and 540 in a normal distribution with a mean of 500 and a standard deviation of 40, you can use the empirical rule, also known as the 68-95-99.7 rule.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean in a normal distribution. Since the standard deviation is 40, one standard deviation below the mean is 500 - 40 = 460 and one standard deviation above the mean is 500 + 40 = 540.
Therefore, approximately 68% of the data is between 460 and 540 in this normal distribution.