Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, it decided to collect some data. Specifically, a random sample of 1,000 passengers was selected. The passengers were observed, and the number of bags carried on the plane was noted. Out of the 1,000 passengers, 345 had more than one bag. The domestic version of Boeing's 747 has a capacity for 568 passengers. Determine an interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane. Assume the plane is at its passenger capacity.
A) (171.651, 216.214)
B) (174.412, 217.218)
C) (181.514, 208.313)
D) (179.20, 212.716)

Question

Quizplus · Accepted Answer

To estimate the interval of passengers expected to carry more than one piece of luggage on a full Boeing 747 (capacity of 568 passengers), we use the proportion of passengers with more than one bag from the sample (345 out of 1000, or 0.345) and apply it to the full capacity. The formula for the confidence interval for a proportion is $p \pm z \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score for the desired confidence level (not provided, but typically 1.96 for 95% confidence), and $n$ is the sample size. Applying this proportion (0.345) to the plane's capacity (568 passengers), we estimate the number of passengers with more than one bag. The specific numbers provided in option D suggest a calculation based on this approach, considering the variability and the size of the plane's capacity.

Most Major Airlines Allow Passengers to Carry Two Pieces of Luggage