Final answer:
Budgeting 1.1 hours might not be enough due to the standard deviation of 1 hour and the nature of variability. By considering the Central Limit Theorem, the 0.1-hour cushion does not provide a strong confidence level that 1.1 hours will always be sufficient. It's recommended to budget more time per unit or calculate a confidence interval for a more accurate estimate.
Step-by-step explanation:
To determine if budgeting an average of 1.1 hours per technician will be enough time to service the air conditioners, we'll need to apply the Central Limit Theorem (CLT) to the given service records. CLT states that when independent random variables are added, their normalized sum tends toward a normal distribution (a 'bell curve') even if the original variables themselves are not normally distributed. Given the average service time is 1 hour and the standard deviation is 1 hour for servicing a unit, we can calculate the mean and standard deviation for our sample of 70 units.
Using CLT, the expected mean for the sample (70 units) is the same as the population mean, hence, 1 hour. The sample standard deviation (σ/√n) would be 1 hour/√70 units, approximately 0.12 hours. If we allocate 1.1 hours per technician, we're only accounting for a 0.1-hour cushion beyond the average.
This may not be enough because there's variability in the individual service times and a single standard deviation includes approximately 68% of the probability. To decrease the risk of underestimating the time needed, it might be wiser to consider budgeting more time per unit, or at least calculate the desired confidence interval to assure that budgeted time will suffice.