Final answer:
The sampling distribution of the mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. The probability that the sample mean is less than a given value can be found by standardizing the value and using a standard normal distribution table. The probability that the sample mean is between two given values can be found by calculating the z-scores for both values and finding the area between those z-scores using the standard normal distribution table.
Step-by-step explanation:
The sampling distribution of the mean is the distribution of all possible sample means that could be obtained from repeated sampling. In this case, the sampling distribution of the mean follows a normal distribution with a mean equal to the population mean (110,000) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (20,200/√500).
To find the probability that the sample mean is less than 98,000 passengers, we can standardize the value using the sampling distribution. The z-score for a sample mean of 98,000 can be calculated as z = (98,000 - 110,000) / (20,200/√500). Using a standard normal distribution table, we can find the corresponding probability.
Similarly, to find the probability that the sample mean is between 102,000 and 104,500 passengers, we can calculate the z-scores for both values using the sampling distribution and find the area between those z-scores using the standard normal distribution table.