Final answer:
A budget of 1.1 hours per technician is likely to be sufficient based on the average service time and standard deviation from previous records, with a consideration for the variability in individual service times.
Step-by-step explanation:
When planning the maintenance schedule for air conditioners, the use of statistical data from previous service records is crucial for efficient time management. Given that the average time spent on servicing each unit is one hour with a standard deviation of one hour, we must consider the variability in service times. By applying the Central Limit Theorem, we can predict the distribution of the sample mean for a simple random sample of 70 units.
To ensure that the budgeted 1.1 hours per technician is sufficient, we can calculate the sample mean's standard deviation, also known as the standard error, which is the population standard deviation divided by the square root of the sample size (n). With a standard deviation of one hour and a sample size of 70, the standard error is 1 / sqrt(70), which equals approximately 0.12 hours, or about 7 minutes.
Now, using the concept of confidence intervals we can deduce if 1.1 hours will likely be enough. The expected mean service time is one hour, and adding three times the standard error (0.12 hours) to account for variability gives us 1.36 hours, suggesting that the upper limit of the service time is likely below 1.1 hours for the majority of the units. On average, budgeting 1.1 hours per technician should be sufficient. However, it's important to also consider that extreme cases can occur, and some units may require more than the budgeted time.