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 63 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 60 and 66?​

Answer 1

Using Empirical data approximate percentage of daily phone calls numbering between 60 and 66  is  68% as data lies with in one standard deviation from mean

Given:

• Bell Shape Data
• Mean = 63
• SD = 3

To Find:

• Using Empirical Formula ,approximate percentage of daily phone calls numbering between 60 and 66

Solution:

• Normal Distribution has bell shape curve
• The Empirical Rule states that in  a normal distribution
• 68% of the data falls with in one standard deviation ( -1 to 1)
• 95%  of data falls with in two standard deviations, and  (-2 to 2)
• 99.7% of data falls with in three standard deviations from the mean. (-3 to 3)
• z score = ( Value - mean)/SD

Step 1:

Calculate z score for 60

Z = (60 - 63)/3

Z = -1

Step 2:

Calculate z score for 66

Z = (66 - 63)/3

Z =  1

Step 3:

As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 60 and 66  is  68%