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 6. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 52 and 76?

Question

Mathematics

Pooch

28 September, 01:50

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 6. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 52 and 76?

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Paris · Answer 1

0.9544 or 95.44%

Step-by-step explanation:

The empirical rule indicates that the percentage of data falls in one standard deviation, 2 standard deviation and 3 standard deviation are 68.26%,95.44% and 99.73%

We are given that x1=52, x2=76, mean=64 and standard deviation=6

mean+sd = 64+6=70

mean-sd=64-6=58

mean+2*sd=64+12=76

mean+2*sd=52

x1 and x2 are within 2 standard deviation and the percentage of data lies between two standard deviation is 95.44%.