Question

3. Suppose travellers purchase airline tickets 20 days before their planned travel date, on average.

a) [2 marks] What is the probability that a traveller will purchase their airline ticket no more than 10 days before their planned travel date?

b) [1 mark] Notice that 10 days is exactly half of 20 days. Why isn’t your probability in part a) equal to 0.5? Please answer in one sentence.

c) [3 marks] What is the probability that a traveller will purchase their airline ticket 17 – 19 days before their planned travel date?

d) [1 mark] What is the probability that a traveller will purchase their airline ticket 18 days before their planned travel date?

Answer 1

The output is:

	20	mean rate of occurrence
		cumulative
X	P(X)	probability
0	0.00000	0.00000
1	0.00000	0.00000
2	0.00000	0.00000
3	0.00000	0.00000
4	0.00001	0.00002
5	0.00005	0.00007
6	0.00018	0.00026
7	0.00052	0.00078
8	0.00131	0.00209
9	0.00291	0.00500
10	0.00582	0.01081
11	0.01058	0.02139
12	0.01763	0.03901
13	0.02712	0.06613
14	0.03874	0.10486
15	0.05165	0.15651
16	0.06456	0.22107
17	0.07595	0.29703
18	0.08439	0.38142
19	0.08884	0.47026
20	0.08884	0.55909
21	0.08461	0.64370
22	0.07691	0.72061
23	0.06688	0.78749
24	0.05573	0.84323
25	0.04459	0.88782
26	0.03430	0.92211
27	0.02541	0.94752
28	0.01815	0.96567
29	0.01252	0.97818
30	0.00834	0.98653
31	0.00538	0.99191
32	0.00336	0.99527
33	0.00204	0.99731
34	0.00120	0.99851
35	0.00069	0.99920
36	0.00038	0.99958
37	0.00021	0.99978
38	0.00011	0.99989
39	0.00006	0.99995
40	0.00003	0.99997
41	0.00001	0.99999
42	0.00001	0.99999
43	0.00000	1.00000
44	0.00000	1.00000
45	0.00000	1.00000
46	0.00000	1.00000
47	0.00000	1.00000
48	0.00000	1.00000
49	0.00000	1.00000
	1.00000
	20.000	expected value
	20.000	variance
	4.472	standard deviation

a) [2 marks] What is the probability that a traveller will purchase their airline ticket no more than 10 days before their planned travel date?

P(X < 10 days) = 0.01081

b) [1 mark] Notice that 10 days is exactly half of 20 days. Why isn’t your probability in part a) equal to 0.5? Please answer in one sentence.

The probability in part a) is not equal to 0.5 because this is a Poisson distribution.

c) [3 marks] What is the probability that a traveller will purchase their airline ticket 17 – 19 days before their planned travel date?

P(17 days < X < 19 days) = 0.24918

d) [1 mark] What is the probability that a traveller will purchase their airline ticket 18 days before their planned travel date?

P(X < 18 days) = 0.38142