Final answer:
Budgeting an average of 1.1 hours per technician for air conditioner maintenance may not be enough, as there is a significant probability that the actual time needed could exceed this, considering the average and standard deviation of servicing times.
Step-by-step explanation:
To determine if budgeting an average of 1.1 hours per technician to service air conditioners will be sufficient, we can use the sample mean and standard deviation to compute the probability that the actual time will exceed this budgeted time. Given an average time of 1 hour with a standard deviation of 1 hour, and assuming a normal distribution, we can calculate a confidence interval or use the Central Limit Theorem to see how a sample mean of 70 units will likely behave.
The Central Limit Theorem tells us that the distribution of the sample means will be approximately normally distributed, with a mean equal to the population mean (1 hour) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (the standard error). For a sample size of 70, the standard error is 1/√70, which is approximately 0.12 hours.
The budgeted time of 1.1 hours is less than one standard deviation above the mean (1 + 0.12), which typically encompasses about 68% of the data in a normal distribution. So, there is a significant probability that the actual time needed could exceed the budgeted time, and therefore, the 1.1 hours per technician may not be enough. It would be more prudent to budget more time per technician or examine the actual distribution of servicing times more closely to make a more informed decision.