I considered the distribution of (question)-(1st answer) time interval among the questions that received at least one answer.  There are about 186600 of such questions in the SEDE database, approximately 87% of all questions. (Thus, multiplying the percentages below by 0.87 will give the percentage among *all* existing questions.) Executive summary of results: 

* 30% of questions were answered in 10 minutes or less
* 50% -- in 23 minutes
* 69% -- in one hour
* 75% -- in 1.5 hours
* 90% -- in 15 hours       
* 95% -- in 3.5 days
* 97% -- in 15 days
* 99% -- in 6 months

Among answered questions, the median time to answer is 23 minutes, as stated above. Among all existing questions, it is about 32 minutes.

The longest it ever took for an answer to be posted is over 38 months; the current record holder is https://math.stackexchange.com/q/4706/ (+1 CW points to dfeuer for posting that compilation-answer).  

The distribution is heavy-tailed enough  that I did not consider computing the mean, etc. The complete set of percentiles is given below. 

I used the simple  query [Question-answer time interval](http://data.stackexchange.com/mathematics/query/154746/question-answer-time-interval) running it four times to get  around the 50000 line restriction. (At first run, enter 0 for `minId`; note the `Id` of the last question retrieved; download the results; repeat with the last question `Id` as parameter. Then merge data in your spreadsheet software.)

I don't feel like slicing the data by tags, time of day, day of week, month of year, phases of Moon, etc. The predictive power of this data is rather weak. The site is growing; its dynamics are different during school semesters and during holidays; some prolific answerers join, others quit or go on hiatus. Questions vary by difficulty and the level of specialization,  which is something that tags do not capture. But if someone feels like slicing the data -- go ahead and fork the query.  

 A question does not have to get lots of views to get answered: it needs to be seen by 1 person with the sufficient expertise, interest in the question, and time available. There is no way to predict when or if such a  person will see the question. Choosing proper tags and informative title, writing a clear question in easy-to-read format,  setting a bounty  if needed -- all of these contribute to success more than pondering statistical tea leaves. 


    %	time in minutes
    min	0
    1	2
    2	2
    3	2
    4	3
    5	3
    6	3
    7	4
    8	4
    9	4
    10	4
    11	5
    12	5
    13	5
    14	5
    15	6
    16	6
    17	6
    18	6
    19	7
    20	7
    21	7
    22	8
    23	8
    24	8
    25	9
    26	9
    27	9
    28	10
    29	10
    30	10
    31	11
    32	11
    33	12
    34	12
    35	13
    36	13
    37	13
    38	14
    39	15
    40	15
    41	16
    42	16
    43	17
    44	18
    45	18
    46	19
    47	20
    48	21
    49	22
    50	23
    51	24
    52	25
    53	26
    54	27
    55	28
    56	30
    57	31
    58	32
    59	34
    60	36
    61	38
    62	40
    63	42
    64	45
    65	47
    66	50
    67	53
    68	56
    69	60
    70	64
    71	69
    72	74
    73	80
    74	86
    75	93
    76	102
    77	112
    78	124
    79	137
    80	152
    81	171
    82	194
    83	223
    84	260
    85	306
    86	367
    87	445
    88	549
    89	683
    90	860
    91	1105
    92	1422
    93	1999
    94	3057
    95	4986
    96	9378
    97	21380
    98	70302
    99	252745
    max	1698418