Chebyshev's theorem is used to describe how much data lies within a particular number of standard deviations, z, of the mean. It states that the proportion of data values within z standard deviations of the mean is at least (1-2), where z is any value greater than 1. This is very powerful because it can be applied to any distribution, regardless of shape. It is given that the average amount of sleep adults get per night is 6.6 hours with a standard deviation of 1.3 hours. We are asked to calculate the percentage of adults who sleep between 2.7 and 10.5 hours. To use Chebyshev's theorem, we must first determine how many standard deviations above and below the mean 10.5 and 2.7 are, respectively. Since the upper value is 10.5 and the mean is 6.6, the upper value is some number of standard deviations above the mean. To find the number of standard deviations z that a value is above the mean, use the following formula. Find z for the upper value. z = value higher than the mean - mean standard deviation value higher than the mean - mean standard deviation 10.5- z = Since the lower value is 2.7 and the mean is 6.6, the lower value is some number of standard deviations below the mean. To find the number of standard deviations z that a value is below the mean, use the following formula. Find z for the lower value. mean - value lower than the mean standard deviation 6.6- mean - value lower than the mean standard deviation 1.3