Chapter 5, Problem 1P

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.

1. 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?
2. 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?
3. 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?
4. d. What is the probability that a randomly selected AirTran Airways flight will not arrive on time?

To determine

Find the probability that a randomly selected D flight has an on-time arrival.

Answer to Problem 1P

The probability that a randomly selected D flight has an on-time arrival is 0.865.

Explanation of Solution

Calculation:

From the given table, the percentage of D flight has an on-time arrival is 86.5%.

Thus, the probability that a randomly selected D flight has an on-time arrival is 0.865.

To determine

Find the probability that a randomly selected airline has less than two mishandled baggage reports per 1,000 passengers.

Answer to Problem 1P

The probability that a randomly selected airline has less than two mishandled baggage reports per 1,000 passengers is 0.3.

Explanation of Solution

Calculation:

From the given table, there are 3 airlines which have less than two mishandled baggage reports per 1,000 passengers. Also, there are 10 airlines.

Define the event A as the airline has less than two mishandled baggage reports per 1,000 passengers.

The required probability is obtained as given below:

$\begin{array}{c}P\left(A\right)=\frac{\left(\begin{array}{l}\text{Number of airlines less than two mishandled }\\ \text{baggage reports per 1,000 passengers}\end{array}\right)}{\text{Total number of airlines}}\\ =\frac{3}{10}\\ =0.3\end{array}$

Thus, the probability that a randomly selected airline has less than two mishandled baggage reports per 1,000 passengers is 0.3.

To determine

Find the probability that a randomly selected airline has more than one customer compliant per 1,000 passengers.

Answer to Problem 1P

The probability that a randomly selected airline has more than one customer compliant per 1,000 passengers is 0.5.

Explanation of Solution

Calculation:

From the given table, there are 5 airlines which have more than one customer compliant.

Define the event B as the airline that has more than one customer compliant per 1,000 passengers.

The required probability is obtained as given below:

$\begin{array}{c}P\left(B\right)=\frac{\left(\begin{array}{l}\text{Number of airlines that has more than }\\ \text{one customer compliant per 1,000 passengers}\end{array}\right)}{\text{Total number of airlines}}\\ =\frac{5}{10}\\ =0.5\end{array}$

Thus, the probability that a randomly selected airline has more than one customer compliant per 1,000 passengers is 0.5.

To determine

Find the probability that a randomly selected AT flight does not have an on-time arrival.

Answer to Problem 1P

The probability that a randomly selected AT flight does not have an on-time arrival is 0.129.

Explanation of Solution

Calculation:

From the given table, the percentage of AT flight has an on-time arrival is 87.1%.

Define the event C as AT flight has an on-time arrival.

The required probability is obtained as given below:

$\begin{array}{c}P\left(C^C\right)=1-P\left(C\right)\\ =1-0.871\\ =0.129\end{array}$

Thus, the probability that a randomly selected AT flight does not have an on-time arrival is 0.129.