In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 48 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 24 and 72? Do not enter the percent symbol. ans = %
- Empirical Rule :
The Empirical Rule states that the area under the normal distribution that is within one standard deviation of the mean is approximately 0.68, the area within two standard deviations of the mean is approximately 0.95, and the area within three standard deviations of the mean is approximately 0.997.
In other words ,
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
In particular, the empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
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