A data distribution has a mean of 10 and a standard deviation of 1. Suppose we do not know if the distribution is
bell-shaped or not. Estimate the proportion of data that falls between 9 and 11.
If the distribution is approximately bell-shaped and follows a normal distribution, we can use the empirical rule to estimate the proportion of data that falls between 9 and 11.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
Since the mean is 10 and the standard deviation is 1, one standard deviation below the mean is 10 - 1 = 9 and one standard deviation above the mean is 10 + 1 = 11.
Thus, approximately 68% of the data falls between 9 and 11.