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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 43 and a standard deviation of 6. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 31 and 55

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Answer:

5% of daily phone calls numbering between 31 and 55.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 43

Standard Deviation, σ = 6

We are given that the distribution of  number of phone calls is a bell shaped distribution that is a normal distribution.

Empirical Formula:

  • Almost all the data lies within three standard deviation from the mean for a normally distributed data.
  • About 68% of data lies within one standard deviation from the mean.
  • About 95% of data lies within two standard deviations of the mean.
  • About 99.7% of data lies within three standard deviation of the mean.

We have to find the percentage of daily phone calls numbering between 31 and 55

We can write:

[tex]31 = 43 - 2(6) = \mu - 2(\sigma)\\55 = 43 + 2(6) = \mu +2(\sigma)[/tex]

Thus, by Empirical rule around 95% of daily phone calls numbering between 31 and 55.

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