1. What fraction of the days in 2004-2004 failed to meet the targeted daily average hold time of 110 econds? Given that the daily average hold time was normally distributed with a mean of 99.67 and a standard deviation of 24.24, what fraction of days where the call center failed to meet the targeted hold time of 110 seconds would you expect?

a) Based on the data in the exhibit 1, the number of days out of target hold time (more than 110 seconds) is 237. And total number of days is 728. Therefore, fraction of days is equal to 237/728 or 0.32. Total number of days | 728 | Number of days within target hold time (110 seconds or less) | 491 | Number of days out of target hold time (more than 110 seconds) | 237 | Fraction of days where the call center failed to meet targeted hold time | 0.3255 | Fraction of days where the call center failed to meet targeted hold time (%) | 33% |

b) Based on the X=X+z*σ equation, we find the value of z.
X=99.67
σ=24.24
Target hold time = 110 seconds

Then, 110 = 99.67 + z * 24.24. From the equation, z is equal to 0.42. Thus fraction of days where the call center failed to meet targeted hold time is equal to 1 - 0.6628 or 0.33. 2. What fraction of the days in April 2005 failed to meet the targeted daily average hold time of 110 seconds? Given that the daily average hold time after process improvements was normally distributed with a mean of 79.50 and a standard deviation of 16.86, what fraction of days where the call center failed to meet the targeted hold time of 110 seconds would you expect?

a) Based on the data in the exhibit 3, the number of days out of target hold time (more than 110 seconds) is 1. And total number of days is 30. Therefore fraction of days is equal to 1/30 or 0.033. Total number of days | 30 | Number of days within target hold time (110 seconds or less) | 29 | Number of days