Final answer:
The traveler is disputing the claim about the variance, as the calculated variance from the traveler's flights exceeds the airline's claimed limit. For testing the average delay, a t-distribution would be used for a small sample, while a normal distribution would be appropriate for a larger sample like 45 flights. So, the correct answer is option b.
Step-by-step explanation:
The traveler is disputing the claim about the variance. According to the information provided, the traveler's 25 flights had an average delay of 22 minutes with a standard deviation of 15 minutes. This standard deviation corresponds to a sample variance of 225 minutes (since variance is the square of the standard deviation), which exceeds the airline's claim of a variance of no more than 150 minutes. The traveler is thus questioning the consistency of the flight delays as expressed by the variance rather than the actual average delay.
If an additional test were done on the claim of the average delay with the given sample size of 25 flights, the appropriate distribution to use would be the t-distribution, because the sample size is small. However, if the sample size were increased to 45 flights, the normal distribution would be more appropriate, as the larger sample size would allow us to invoke the Central Limit Theorem.
So, the correct answer is option b.