Final answer:
For an additional test on the claim of the average flight delay with a known population standard deviation, the normal distribution is used; otherwise, with an unknown standard deviation and a large sample size, the t-distribution is appropriate.
Step-by-step explanation:
If an additional test were done on the claim of the average delay, and assuming that the population standard deviation is unknown and the sample is sufficiently large or the sample data are approximately normally distributed, you would use the c-distribution. In instances where you know the population standard deviation, you would use the normal distribution for the hypothesis test. However, when the standard deviation is unknown and the sample size is less than 30, or the data do not come from a normal distribution but the sample size is large enough (usually n > 30), the t-distribution should be used instead.
For example, if 45 flights were surveyed to test the claim of the average delay, and the population standard deviation was unknown, you would use the t-distribution. This is because the central limit theorem states the sampling distribution of the sample mean will be approximately normal if the sample size is large enough, and 45 is considered large enough for this theorem to hold.