Read this carefully! Explanation of the Flights Data

The data set contains all the 243 United Airlines flights that departed Houston in July 2011. For each flight, we are given the following information:

DayofMonth = day of the month

DayOfWeek = day of the week of departure starting with Monday (1 = Monday, 2 = Tuesday, ..., 7 = Sunday)

FlightNum = number identifying the flight

Dest = destination airport code (DEN = Denver, IAD = Washington DC, ORD = Chicago, SFO = San Francisco)

Distance = distance of flight, in miles

DepDelay = departure delay in minutes (negative value indicates the flight departed earlier than the scheduled time)

ArrDelay = arrival delay in minutes (negative value indicates the flight arrived at its destination earlier than the scheduled time)

For example, the first flight in the data corresponds to the United Airlines flight # 230 that flew from Houston to Chicago on July 1, 2011, Friday. This flght, covering distance of 925 miles, departed 14 minutes later than the scheduled time and arrived in Chicago 15 minutes later than the scheduled time.

As another example, the 3rd flight in the data, UA flight #415 flying to Denver departed on time (DepDelay = 0) and arrived in Denver 11 minutes earlier than the scheduled time (ArrDelay = -11).

a) If the destination of a flight is known to be Chicago, what is the probabiltiy that there will be arrival delay of less than 40 mins?

b) Find the probability that a flight will arrive on or before scheduled time if the destination of the flight is known to be San Francisco. (Read the description of the ArrDelay variable carefully)

c) What is the probability that any randomly selected United flight will have less than 40 mins arrival delay?

DayOfWeek	FlightNum	Dest	Distance	DepDelay	ArrDelay
5	230	ORD	925	14	15
5	363	SFO	1635	11	2
5	415	DEN	862	0	-11
5	750	ORD	925	205	204
5	774	DEN	862	3	-21
5	801	DEN	862	107	106
5	993	IAD	1190	1	0
5	995	IAD	1190	13	21
6	221	ORD	925	-3	14
6	286	DEN	862	2	-11
6	344	DEN	862	1	-6
6	434	SFO	1635	-1	-8
6	624	ORD	925	-3	-12
6	734	ORD	925	4	-4
6	772	ORD	925	-2	-6
6	855	SFO	1635	-1	-14
7	278	ORD	925	-1	-1
7	322	SFO	1635	-2	0
7	338	ORD	925	5	11
7	357	DEN	862	3	-17
7	410	DEN	862	14	16
7	425	ORD	925	6	27
7	648	ORD	925	0	-1
7	819	DEN	862	1	-19
7	855	SFO	1635	-1	-5
7	995	IAD	1190	10	9
1	230	ORD	925	3	-2
1	309	DEN	862	1	-14
1	319	SFO	1635	-4	-9
1	774	DEN	862	0	-24
1	830	ORD	925	3	24
1	855	SFO	1635	169	149
1	993	IAD	1190	-1	23
1	995	IAD	1190	-5	-9
2	230	ORD	925	19	35
2	434	SFO	1635	11	6
2	677	DEN	862	0	-22
2	774	DEN	862	-5	-29
2	801	DEN	862	0	-5
2	855	SFO	1635	5	4
2	993	IAD	1190	-4	-13
2	995	IAD	1190	-2	-9
3	230	ORD	925	12	23
3	363	SFO	1635	-7	-12
3	373	DEN	862	0	-11
3	415	DEN	862	-1	-21
3	774	DEN	862	-4	1
3	855	SFO	1635	29	1
3	993	IAD	1190	-5	5
3	995	IAD	1190	-7	-20
4	326	DEN	862	-1	-9
4	363	SFO	1635	0	-10
4	415	DEN	862	1	-20
4	730	ORD	925	3	-6
4	774	DEN	862	0	10
4	855	SFO	1635	8	-3
4	993	IAD	1190	30	31
4	995	IAD	1190	-7	-6
5	415	DEN	862	6	-13
5	434	SFO	1635	-6	-15
5	730	ORD	925	4	10
5	774	DEN	862	-5	-9
5	841	DEN	862	-1	-10
5	855	SFO	1635	4	3
5	993	IAD	1190	11	10
5	995	IAD	1190	-2	11
6	221	ORD	925	1	-7
6	286	DEN	862	0	-16
6	314	DEN	862	3	3
6	325	ORD	925	-5	-9
6	434	SFO	1635	-3	3
6	624	ORD	925	13	1
6	855	SFO	1635	63	56
7	311	ORD	925	27	6
7	420	ORD	925	-2	-20
7	434	SFO	1635	-4	-10
7	774	DEN	862	-4	-21
7	819	DEN	862	2	-14
7	841	DEN	862	5	-1
7	855	SFO	1635	86	85
7	995	IAD	1190	-3	-21
1	301	DEN	862	56	47
1	311	ORD	925	4	-11
1	434	SFO	1635	2	3
1	774	DEN	862	148	121
1	855	SFO	1635	6	76
1	992	DEN	862	1	-18
1	993	IAD	1190	-6	-18
1	995	IAD	1190	-1	-3
2	301	DEN	862	0	2
2	311	ORD	925	0	9
2	415	DEN	862	20	3
2	434	SFO	1635	0	5
2	774	DEN	862	0	75
2	855	SFO	1635	0	8
2	995	IAD	1190	0	-1
3	311	ORD	925	21	33
3	415	DEN	862	-2	-18
3	434	SFO	1635	1	5
3	739	DEN	862	-1	-6
3	774	DEN	862	121	117
3	855	SFO	1635	6	8
3	993	IAD	1190	-1	-6
3	995	IAD	1190	4	23
4	311	ORD	925	13	16
4	415	DEN	862	2	-13
4	434	SFO	1635	0	-8
4	739	DEN	862	10	1
4	774	DEN	862	0	-19
4	855	SFO	1635	-3	52
4	993	IAD	1190	-5	0
5	311	ORD	925	7	5
5	415	DEN	862	0	-20
5	434	SFO	1635	34	43
5	739	DEN	862	16	8
5	774	DEN	862	-4	-32
5	855	SFO	1635	5	24
5	993	IAD	1190	15	22
5	995	IAD	1190	-5	-4
6	221	ORD	925	7	4
6	286	DEN	862	-1	-18
6	434	SFO	1635	5	5
6	462	ORD	925	-2	9
6	624	ORD	925	1	-6
6	667	DEN	862	3	-3
6	855	SFO	1635	10	27
7	256	ORD	925	96	126
7	420	ORD	925	-2	-7
7	434	SFO	1635	-2	-20
7	774	DEN	862	3	-16
7	801	DEN	862	2	4
7	819	DEN	862	3	-16
7	855	SFO	1635	-1	37
7	995	IAD	1190	-6	-10
1	434	SFO	1635	-3	-20
1	730	ORD	925	-2	-2
1	774	DEN	862	26	13
1	841	DEN	862	80	64
1	855	SFO	1635	3	-4
1	992	DEN	862	1	-18
1	993	IAD	1190	-11	0
1	995	IAD	1190	1	7
2	415	DEN	862	-4	-23
2	434	SFO	1635	-4	-1
2	730	ORD	925	8	6
2	774	DEN	862	-3	-20
2	801	DEN	862	15	16
2	855	SFO	1635	27	39
2	993	IAD	1190	59	64
2	995	IAD	1190	3	20
3	415	DEN	862	16	10
3	434	SFO	1635	-1	-8
3	730	ORD	925	98	87
3	774	DEN	862	-4	-20
3	841	DEN	862	-1	-14
3	855	SFO	1635	117	115
3	993	IAD	1190	-1	-4
3	995	IAD	1190	0	-4
4	230	ORD	925	4	-11
4	415	DEN	862	29	9
4	434	SFO	1635	3	-8
4	774	DEN	862	-4	-18
4	841	DEN	862	-2	-19
4	855	SFO	1635	2	-2
4	993	IAD	1190	5	-2
4	995	IAD	1190	-1	9
5	415	DEN	862	-1	-19
5	434	SFO	1635	-2	1
5	439	ORD	925	6	-2
5	774	DEN	862	141	114
5	841	DEN	862	168	164
5	855	SFO	1635	67	48
5	993	IAD	1190	-3	16
5	995	IAD	1190	0	1
6	221	ORD	925	-1	-15
6	286	DEN	862	-5	-23
6	434	SFO	1635	-7	-20
6	462	ORD	925	-1	-4
6	624	ORD	925	202	193
6	667	DEN	862	124	107
6	855	SFO	1635	4	-5
7	420	ORD	925	0	17
7	434	SFO	1635	-2	-11
7	439	ORD	925	2	4
7	774	DEN	862	143	107
7	801	DEN	862	99	103
7	819	DEN	862	0	-16
7	855	SFO	1635	40	9
7	995	IAD	1190	-5	-6
1	434	SFO	1635	-3	0
1	439	ORD	925	49	50
1	774	DEN	862	10	0
1	841	DEN	862	2	11
1	855	SFO	1635	57	44
1	992	DEN	862	-1	-18
1	993	IAD	1190	-3	9
1	995	IAD	1190	5	12
2	415	DEN	862	18	8
2	434	SFO	1635	0	-8
2	439	ORD	925	99	105
2	774	DEN	862	2	-11
2	801	DEN	862	-4	-12
2	855	SFO	1635	23	6
2	993	IAD	1190	32	23
2	995	IAD	1190	4	15
3	415	DEN	862	-4	-23
3	434	SFO	1635	-4	-11
3	439	ORD	925	28	24
3	774	DEN	862	-5	-14
3	841	DEN	862	-1	-16
3	855	SFO	1635	58	54
3	993	IAD	1190	-2	-16
3	995	IAD	1190	-4	-10
4	415	DEN	862	-2	-16
4	434	SFO	1635	2	-21
4	439	ORD	925	2	31
4	774	DEN	862	4	0
4	841	DEN	862	4	12
4	855	SFO	1635	4	1
4	993	IAD	1190	-4	-17
4	995	IAD	1190	-3	-5
5	415	DEN	862	-2	-19
5	434	SFO	1635	34	31
5	439	ORD	925	149	130
5	774	DEN	862	31	18
5	841	DEN	862	68	57
5	855	SFO	1635	-5	-7
5	993	IAD	1190	15	52
5	995	IAD	1190	-1	-5
6	221	ORD	925	0	2
6	286	DEN	862	-2	-13
6	434	SFO	1635	0	-16
6	462	ORD	925	-3	-15
6	624	ORD	925	7	4
6	667	DEN	862	45	32
6	855	SFO	1635	91	85
7	420	ORD	925	-3	-10
7	434	SFO	1635	75	72
7	439	ORD	925	76	74
7	801	DEN	862	21	28
7	819	DEN	862	0	-17
7	855	SFO	1635	59	70
7	995	IAD	1190	-3	-18