mid size company the distribution of the number of phone calls answered each day by each of the 12 receptionist is bell shaped and has a mean of 50 and standard deviation of 8 using empirical rule what is the approximate percentage of daily phone calls numbering between 34 and 66
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this case, we want to find the percentage of phone calls between 34 and 66, which is within one standard deviation above and below the mean.
So, we need to find the z-scores for 34 and 66, using the formula:
z = (x - μ) / σ
where x is the value (34 or 66), μ is the mean (50), and σ is the standard deviation (8).
For 34:
z = (34 - 50) / 8
z = -2
For 66:
z = (66 - 50) / 8
z = 2
Now, we can look up the percentage of data within -2 and 2 standard deviations from the mean in a standard normal distribution table. This is approximately 68%.
Therefore, the approximate percentage of daily phone calls numbering between 34 and 66 is 68%.