Per the Central Limit Theorem, for any population distribution, the sampling distribution of means is approximately normal for sample sizes exceeding 30 with mean = population mean and standard error = population standard deviation / square root of sample size if the sample size is less than 10% of the population.
The CLT can be applied to this problem as the sample size is 45, which is less than 10% of the total amount of flights.
Given the population standard deviation is 3.4, the standard error of the mean = 3.4 / square root 45 = 0.51:
Because we know the population standard deviation, we can use the z-statistic to compute the probability:
p( sample mean > 12) =
p (z > sample mean - population mean / standard error) = P(Z > 12 - 10 / 0.51) = P(Z > 3.92) ~= 0
