Operations Math Problem: Quality Wireless

Case - Operations Math Problem: Quality Wireless
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Attachment 1
[1]What fraction of the days in 2003-2004 failed to meet the targeted hold time of 110 seconds? 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?
Analysis
Z=x- μ/ σ
The targeted hold time (x) 110 seconds
Daily average hold time (μ) is 99.67 seconds
Standard Deviation (σ) is 24.24 seconds
Hence Z=110-99.67/24.24= 0.426155=0.43
At the 0.05 significance level, the P-Value is 0.33the result is not significant at p < 0.05.
Answer
As such a the fraction representing the days when the call center failed to meet the set time
= 1/3
Based on the assumptions that they workers worked all days the total number of days is 731(365+366)
=1/3*731= 244 days
[2] What fraction of the days in April 2005 failed to meet the targeted 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?
Analysis
Z=x- μ/ σ
The targeted hold time (x) 110 seconds
Daily average hold time (μ) is 79.50 seconds
Standard Deviation (σ) is 16.86 seconds
Z=110-79.50/16.86= 1.809015=1.81
The P-Value is 0.0351The result is significant at p < 0.05.
Answer
The fraction is 1/28.5 (0.0351) is the fraction that the call center did not the set target for the month of April 2005.
[3] Based on the performance in April 2005, do you think that the p...