Final answer:
The probability that the average maintenance time exceeds 1.2 hours for a sample of 81 air-conditioning units is found using the Central Limit Theorem and standard normal distribution, resulting in a probability of approximately 0.0359.
Step-by-step explanation:
The probability that a random sample of 81 air-conditioning units will have an average preventative maintenance time greater than 1.2 hours can be calculated using the Central Limit Theorem.
Since the sample size is large (n=81), the sampling distribution of the sample mean will be approximately normally distributed (by the Central Limit Theorem) even though the population distribution is extremely right skewed.
The mean of the sampling distribution is equal to the population mean (1 hour), and its standard deviation is equal to the population standard deviation (1 hour) divided by the square root of the sample size, which is 1/√81 = 1/9 hours.
To find the probability that the sample mean is greater than 1.2 hours, we calculate the z-score for 1.2, which is (1.2 - 1) / (1/9) = 1.8. We then use the standard normal distribution to find the probability that a z-score is above 1.8. Using standard normal distribution tables or a calculator, we find this probability to be approximatly 0.0359. Therefore, the correct answer is A.