Question
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 64 and a standard deviation of 9. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 37 and 91 ? Do not enter the percent symbol. ans =
Ask by Graham Hall. in the United States
Feb 27,2025
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Answer
99.7
Solution
Using the empirical rule, approximately 99.7 of the data lies within 3 standard deviations of the mean in a bell-shaped distribution.
Here, the lower bound is 37 and the upper bound is 91. The mean is 64 and the standard deviation is 9.
Calculate the z-scores:
For 37: (37 - 64) / 9 = -3
For 91: (91 - 64) / 9 = 3
Since the interval from -3 to 3 standard deviations covers about 99.7 of the observations, the answer is 99.7.
Thus, the approximate percentage of daily phone calls is 99.7.
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To find the approximate percentage of daily phone calls answered between 37 and 91 using the empirical rule, we first need to determine how many standard deviations these values are away from the mean. The mean is 64, and the standard deviation is 9. 1. For 37: \( 37 - 64 = -27 \) \( \frac{-27}{9} = -3 \text{ standard deviations} \) 2. For 91: \( 91 - 64 = 27 \) \( \frac{27}{9} = 3 \text{ standard deviations} \) According to the empirical rule, approximately 99.7% of data falls within 3 standard deviations of the mean. Thus, the approximate percentage of daily phone calls numbering between 37 and 91 is 99.7. ans = 99.7
