Question

a which airline has the higher percentage of on - time flights to the five cities?

excelsior airlines has the higher percentage of on - time flights

b calculate the percentage of on - time flights for the two airlines over all five cities.

over all five cities, excelsior airlines had an on - time percentage of 88 % and paradise airlines had an on - time percentage of 90 %

(round to the nearest tenth as needed.)

c explain the apparent inconsistency in the results.

airlines had the higher on - time percentage in the five cities individually, while airlines had the higher overall on - time percentage. this inconsistency is because most of paradise airlines flights arrive in where they have a percentage of on - time flights. most of excelsior airlines flights landed in where they have a percentage of on - time flights

Explanation:

Step1: Calculate on - time flights for Excelsior Airlines

Multiply the percentage of on - time flights by the number of arrivals for each city and sum them up.
For Los Angeles: \(0.884\times408 = 360.672\)
For Phoenix: \(0.971\times159=154.389\)
For San Diego: \(0.944\times246 = 232.224\)
For San Francisco: \(0.883\times533=470.639\)
For Seattle: \(0.865\times2185 = 1890.025\)
Total on - time flights for Excelsior Airlines: \(360.672 + 154.389+232.224 + 470.639+1890.025=3107.949\)
Total arrivals for Excelsior Airlines: \(408 + 159+246+533+2185=3531\)
Percentage of on - time flights for Excelsior Airlines: \(\frac{3107.949}{3531}\times100\%\approx88\%\)

Step2: Calculate on - time flights for Paradise Airlines

Multiply the percentage of on - time flights by the number of arrivals for each city and sum them up.
For Los Angeles: \(0.854\times728 = 622.612\)
For Phoenix: \(0.927\times5137=4762.09\)
For San Diego: \(0.838\times468 = 392.204\)
For San Francisco: \(0.767\times349 = 267.683\)
For Seattle: \(0.718\times171=122.778\)
Total on - time flights for Paradise Airlines: \(622.612+4762.09+392.204 + 267.683+122.778=6167.367\)
Total arrivals for Paradise Airlines: \(728+5137+468+349+171 = 6853\)
Percentage of on - time flights for Paradise Airlines: \(\frac{6167.367}{6853}\times100\%\approx90\%\)

Answer:

Paradise Airlines has a higher percentage of on - time flights to the five cities.