Final answer:
Using the sample mean and standard deviation, the standard error is calculated for servicing air conditioners. A z-score is then computed to determine if the budgeted 1.1 hours per technician is adequate. The positive z-score suggests it may be sufficient, but further analysis is recommended.
Step-by-step explanation:
To determine if the budgeted time of 1.1 hours per technician is sufficient to service the air conditioners, we can use the sample mean and standard deviation provided. We know the average time spent on servicing each unit is one hour with a standard deviation of one hour. If a simple random sample of 70 units is taken, we can calculate the standard error of the sample mean using the formula standard error = standard deviation / sqrt(n), where n is the sample size. The standard error would be 1 / sqrt(70), which is approximately 0.12 hours.
Next, we apply the Central Limit Theorem, which states that the distribution of sample means will be normally distributed, given a sufficiently large sample size (in this case, 70). We want to find out if the budgeted 1.1 hours is enough. The z-score can be calculated using (budgeted time - population mean) / standard error. That would give us (1.1 - 1) / 0.12, which equals approximately 0.83.
The z-score tells us how many standard deviations the budgeted time is away from the mean. A z-score of 0.83 corresponds to being above the mean, which suggests that 1.1 hours might be an adequate average amount of time per technician since it's higher than the average service time of 1 hour. However, to make a more informed decision, the company could check the z-score against standard normal distribution tables to understand the probability of this allowance being sufficient to cover the work or decide if an adjustment is needed based on acceptable risk levels.