#Empirical rule percentages plus#

#Empirical rule percentages plus#

So, 99.7% of the data will fall between the mean μ plus or minus 3 times the standard deviation σ. The third part of the rule states that 99.7% of the data falls between these two values: So, 95% of the data will fall between the mean μ plus or minus 2 times the standard deviation σ. The second part of the rule states that 95% of the data falls between these two values:

Thus, 68% of the data will fall between the mean μ plus or minus the standard deviation σ. The first part of the rule states that 68% of the data falls between these two values: The empirical rule can be represented in three parts using the following formulas: The standard deviation is a measure of the variability within the data and is represented using the greek letter sigma σ. If you’re just getting started with statistics, the mean is the average value of the data set and is often represented using the greek letter mu μ. 99.7% of the data falls within three standard deviations of the mean.95% of the data falls within two standard deviations of the mean.68% of the data falls within one standard deviation of the mean.Thus statement (6) must definitely be correct. Statement (4) is definitely correct and statement (4) implies statement (6): even if every measurement that is outside the interval (675,775) is less than 675 (which is conceivable, since symmetry is not known to hold), even so at most 25% of all observations are less than 675.But this is not stated perhaps all of the observations outside the interval (675,775) are less than 75. This would be correct if the relative frequency histogram of the data were known to be symmetric. Statement (5) says that half of that 25% corresponds to days of light traffic. Statement (4), which is definitely correct, states that at most 25% of the time either fewer than 675 or more than 775 vehicles passed through the intersection.Statement (4) says the same thing as statement (2) but in different words, and therefore is definitely correct.Thus statement (3) is definitely correct. Statement (3) says the same thing as statement (2) because 75% of 251 is 188.25, so the minimum whole number of observations in this interval is 189.Statement (2) is a direct application of part (1) of Chebyshev’s Theorem because ( x - − 2 s, x - + 2 s ) = ( 675,775 ).Get instant feedback, extra help and step-by-step explanations. Statement (1) is based on the Empirical Rule and therefore it might not be correct. Practice Using the Empirical Rule to Identify Percentages of a Normal Distribution with practice problems and explanations. Since it is not stated that the relative frequency histogram of the data is bell-shaped, the Empirical Rule does not apply.On at most 25% of the weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m.On at most 12.5% of the weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m.was either less than 675 or greater than 775. On at least 189 weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m.On at least 75% of the weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m.

On approximately 95% of the weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m.Identify which of the following statements must be true. The sample mean is x - = 725 and the sample standard deviation is s = 25. was observed and recorded on every weekday morning of the last year. The number of vehicles passing through a busy intersection between 8:00 a.m. These tallies are not coincidences, but are in agreement with the following result that has been found to be widely applicable. All of the measurements are within three standard deviations of the mean, that is, between 69.92 − 3 ( 1.70 ) = 64.822 and 69.92 + 3 ( 1.70 ) = 75.02 inches. If we count the number of observations that are within two standard deviations of the mean, that is, that are between 69.92 − 2 ( 1.70 ) = 66.52 and 69.92 + 2 ( 1.70 ) = 73.32 inches, there are 95 of them. If we go through the data and count the number of observations that are within one standard deviation of the mean, that is, that are between 69.92 − 1.70 = 68.22 and 69.92 + 1.70 = 71.62 inches, there are 69 of them. The mean and standard deviation of the data are, rounded to two decimal places, x - = 69.92 and s = 1.70. A relative frequency histogram for the data is shown in Figure 2.15 'Heights of Adult Men'. Table 2.2 'Heights of Men' shows the heights in inches of 100 randomly selected adult men. We start by examining a specific set of data.