Answer of Discussion Questions
Q1. Given,
The mean daily hold time μ = 99.67 s; Standard Deviation σ = 24.24 s
The targeted hold time x = 110 s
The fraction of days when hold time exceeded 110 s = P(x>110) = ?
Answer:
Mean of a distribution (μ) and a data point (x) is related by the following equation: x = μ ± zσ
For x > 110 s; [pic]
Now, [pic]
Value of [pic] is area under normal curve between z = 0 to z = 0.43.
Thus it can be seen that fraction of days when call center failed to meet the targeted hold time is approximately 1/3 or 0.336. This finding is supported from the frequency distribution table as well where this fraction is 240/731 ~1/3.
Q2. Given,
The mean daily hold time μ = 79.50 s; Standard Deviation σ = 16.86 s
The targeted hold time x = 110 s
The fraction of days when hold time exceeded 110 s = P(x>110) = ?
Answer:
Mean of a distribution (μ) and a data point (x) is related by the following equation: x = μ ± zσ
For x > 110 s; [pic]
Now, [pic]
Value of [pic] is area under normal curve between z = 0 to z = 1.81.
Thus it can be seen that fraction of days when call center failed to meet the targeted hold time is approximately 1/30 or 0.0351. This finding is supported from the frequency distribution table as well where this fraction is 1/30.
Q3. If one examines the performance of the call centre during 2003 – 2004, he finds that every third day the targeted hold time of 110 s. This has been confirmed by the statistical analysis as well as from the frequency distribution table of the hold time during that period. This was naturally a major concern as customers do not like to be on hold for vary long time and therefore, a call centre cannot afford to fail on the targeted hold time every third day. Due to this a major corrective action was taken based on the findings and recommendation of the task force. After implementing the