the table to the right shows the arrival data for two airlines in five cities. complete parts (a) through (c) below
(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) compute 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 85.1% and paradise airlines had an on - time percentage of 90%
(round to the nearest tenth as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Calculate the weighted average for Excelor Airlines
The formula for weighted - average is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$, where $x_{i}$ is the percentage of on - time flights and $f_{i}$ is the number of flights.
For Excelor Airlines:
$$
\begin{align*}
\sum_{i = 1}^{5}x_{i}f_{i}&=(93.9\%\times440)+(95.2\%\times132)+(94.2\%\times272)+(87.2\%\times649)+(80.8\%\times2091)\
&=(0.939\times440)+(0.952\times132)+(0.942\times272)+(0.872\times649)+(0.808\times2091)\
& = 413.16+125.664 + 256.224+565.928+1695.528\
&=3056.5
\end{align*}
$$
$\sum_{i = 1}^{5}f_{i}=440 + 132+272+649+2091=3584$
The weighted - average $\bar{x}_{Excelor}=\frac{3056.5}{3584}\approx85.3\%$

## Step2: Calculate the weighted average for Paradise Airlines
$$
\begin{align*}
\sum_{i = 1}^{5}x_{i}f_{i}&=(89.9\%\times865)+(92.6\%\times5234)+(82.0\%\times306)+(70.5\%\times278)+(75.3\%\times714)\
&=(0.899\times865)+(0.926\times5234)+(0.82\times306)+(0.705\times278)+(0.753\times714)\
&=777.635+4846.684+250.92+196.99+537.642\
&=7009.871
\end{align*}
$$
$\sum_{i = 1}^{5}f_{i}=865 + 5234+306+278+714=7397$
The weighted - average $\bar{x}_{Paradise}=\frac{7009.871}{7397}\approx94.8\%$

# Answer:
Paradise Airlines has a higher percentage of on - time flights.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the weighted average for Excelor Airlines

Step2: Calculate the weighted average for Paradise Airlines

Answer: