HW 3
1. 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
Virgin America
JetBlue
AirTran Airways
Delta Air Lines
Alaska Airlines
Frontier Airlines
Southwest Airlines
US Airways
American Airlines
United Airlines
On-Time Arrivals
(%)
83.5
79.1
87.1
86.5
87.5
77.9
83.1
85.9
76.9
77.4
Mishandled Baggage
per 1,000 Passengers
0.87
1.88
1.58
2.10
2.93
2.22
3.08
2.14
2.92
3.87
Customer Complaints
per 1,000 Passengers
1.50
0.79
0.91
0.73
0.51
1.05
0.25
1.74
1.80
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?
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?
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?
d. What is the probability that a randomly selected AirTran Airways flight will not arrive on time?
2. Suppose that for a recent admissions class, an Ivy League college received 2,851 applications
for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and
deferred 964 to the regular admission pool for further consideration. In the past, this school has
admitted 18% of the deferred early admission applicants during the regular admission process.
Counting the students admitted early and the students admitted during the regular admission
process, the total class size was 2,375. Let E, R, and D represent the events that a student who
applies for early admission is admitted early, rejected outright, or deferred to the regular
admissions pool.
a. Use the data to estimate P(E), P(R), and P(D).
b. Are events E and D mutually exclusive? Find (P ∩ D)
c. For the 2,375 students who were admitted, what is the probability that a randomly selected
student was accepted during early admission?
3. Suppose that we have two events, A and B, with P(A) = 0.50, P(B) = 0.60 and P(A ∩ B) = 0.40.
a. Find P(A l B)
b. Find P(B l A)