Question

On-time arrivals, lost baggage, and customer complaints are three measures that are typically used to measure the quality of service being offered by airlines. Suppose that the following values represent the on-time arrival percentage, amount of lost baggage, and customer complaints for 10 U.S. airlines.

Airline	On-Time Arrivals (%)	Mishandled Baggage per 1,000 Passengers	Customer Complaints per 1,000 Passengers
Virgin America	83.5	0.87	1.50
JetBlue	79.1	1.88	0.79
AirTran Airways	87.1	1.58	0.91
Delta Air Lines	86.5	2.10	0.73
Alaska Airlines	87.5	2.93	0.51
Frontier Airlines	77.9	2.22	1.05
Southwest Airlines	83.1	3.08	0.25
US Airways	85.9	2.14	1.74
American Airlines	76.9	2.92	1.80
United Airlines	77.4	3.87	4.24

(a)	Based on the data above, if you randomly choose a Delta Air Lines flight, what is the probability that this individual flight will have an on-time arrival? If required, round your answer to three decimal places.
(b)	If you randomly choose 1 of the 10 airlines for a follow-up study on airline quality ratings, what is the probability that you will choose an airline with less than two mishandled baggage reports per 1,000 passengers? If required, round your answer to two decimal places.
(c)	If you randomly choose 1 of the 10 airlines for a follow-up study on airline quality ratings, what is the probability that you will choose an airline with more than one customer complaint per 1,000 passengers? If required, round your answer to two decimal places.
(d)	What is the probability that a randomly selected AirTran Airways flight will not arrive on time? If required, round your answer to three decimal places.

Answer 1

Concepts and reason

The concept of probability is used to solve here to solve this problem.

The likelihood of occurring of an event is called probability. Probability provides a measure of how likely that an event occurs.

The probability of an event lies between 0 and 1. It should be positive and can take the form of fractions, decimals between 0 and 1. It can take the form of percentages between 1 to 100.

Fundamentals

The general formula for probability is,

$\begin{array}{c}\\P\left( E \right) = \frac{{{\rm{Number of favorable outcomes}}}}{{{\rm{Total number of outcomes}}}}\\\\ = \frac{{n\left( E \right)}}{{n\left( S \right)}}\\\end{array}$

The probability, P for the complementary event can be calculated as:

$P\left( {{E^c}} \right) = 1 - P\left( E \right)$

Here, ${E^c}$ is the complimentary event of event $E$ .

(a)

According to the provided information, the sample size, n is equal to 10 and the on-time arrival of the Delta Airlines flight is 86.5%.

Therefore, the probability that the Delta Airlines flight will have an on-time arrival is equal to 86.5% or 0.865.

(b)

According to the provided information, the sample size, n is equal to 10 and the number of airlines with less than two mishandles baggage reports per 1000 passengers are 3.

Therefore, the probability can be calculated as:

$\begin{array}{c}\\P\left( \begin{array}{l}\\{\rm{airlines with less than two}}\\\\{\rm{ mishandles baggage reports}}\\\end{array} \right) = \frac{{\left( \begin{array}{l}\\{\rm{number}}\;{\rm{of}}\;{\rm{airlines with less than }}\\\\{\rm{two mishandles baggage reports}}\\\end{array} \right)}}{{{\rm{total number of airlines}}}}\\\\ = \frac{3}{{10}}\\\\ = 0.3\\\end{array}$

(c)

According to the provided information, the sample size, n is equal to 10 and the number of airlines with more than one customer complaint reports per 1000 passengers are 5.

Therefore, the probability can be calculated as:

$\begin{array}{c}\\P\left( \begin{array}{l}\\{\rm{airlines with more than one }}\\\\{\rm{customer complaint reports}}\\\end{array} \right) = \frac{{\left( \begin{array}{l}\\{\rm{number}}\;{\rm{of}}\;{\rm{airlines with more than }}\\\\{\rm{one customer complaint reports}}\\\end{array} \right)}}{{{\rm{total number of airlines}}}}\\\\ = \frac{5}{{10}}\\\\ = 0.5\\\end{array}$

(d)

According to the provided information, the sample size, n is equal to 10 and the probability of on-time arrival of the AirTran Airways flight is 0.871.

Therefore, the probability can be calculated as:

$\begin{array}{c}\\P\left( {{\rm{flight will not arrive on time}}} \right) = 1 - P\left( {{\rm{flight will arrive on time}}} \right)\\\\ = 1 - 0.871\\\\ = 0.129\\\end{array}$

Ans: Part a

The probability that the Delta Airlines flight will have an on-time arrival is 0.865.

Part b

The probability that the chosen airline with less than two mishandles baggage reports per 1000 passengers is 0.3.

Part c

The probability that the chosen airline with more than one customer complaint reports per 1000 passengers is 0.5.

Part d

The probability that the selected AirTran Airways flight will not arrive on-time is 0.129.