Driving Test

Capt'n Midnight

http://www.drivingtest.ie/drivingtest/HTMLContent/frameset.html
The average pass rate is 54.5%
Average waiting time is 37.8 weeks

Assume that fail rates on retests are the same and the 45.5% who fail each time have to wait the average time each time..

Is the average time for an Irish driver to pass the test over a year or not ?

seamus

Well, you can begin to break it down.

54.5% of people will pass in 37.8 weeks waiting (avg).

24.8% of people will pass in 75.6 weeks. (second try)

11.28% of people will pass in 113.4 weeks. (third try).

We'll ignore people that it takes > 4 goes to get it.

It works out at around 57.5 weeks. That is, on average, people who pass their test within 3 goes, will wait 57.5 weeks for each test. You can't get an actual average because you have to assume that some people will never pass their test.

It all depends on how you look at the data. The average wait time for people who pass within two goes drops ot 49.6 weeks.

Capt'n Midnight

hang on it's exponential decay - A=Ao^ekt

http://math.usask.ca/emr/examples/expdeceg.html
0.545= e^(37.8 weeks) k
k= (ln 0.545)/37.8 = -0.016057

half life t= 0.693 /(-0.016057) = 43.168 weeks

so on average HALF pass the test every 43.168 weeks

doesn't this mean that the AVERAGE waiting time is twice this ?
= 86.336 weeks
= 604 days
= 1 year 8 months !

*Angel*

OK so I agree with you on the half life being 43.168 weeks, but doesn't that mean that half of the original will on average pass in 43.168 weeks and then half of the remaineder will pass in another 43.168 weeks (i.e 86.336 weeks) and so on. So isn't it a sum to infinity???

Although that isn't taking into account that generally it wouldn't take more than a few times to pass. But given the info, taking just the maths shouldn't the above be the case?

By attempt:

1/2(43.168) + 1/4(86.336) + 1/8(129.504) + 1/16(172.672) + 1/32(215.84) + .......

The average pass rate would without a doubt be over a year!!!

*Angel*

Sorry, I just copped on YOU'RE RIGHT!!! (OF COURSE) I'M WRONG, at least I'm the first to admit it, I realise that it would approach 86.336.

Sorry my bad, I shouldn't have questioned you.......

delancde

Yeah, exponential decay is tough. However, it is a really is used in a lot of real-world scenarios.

Application of exponential growth and decay: http://www.brightstorm.com/d/math/s/algebra-2/u/inverse-exponential-and-logarithmic-functions/t/exponential-growth-and-decay

LeixlipRed

This thread is almost 5 years old. Any real need to repopen it??

RoundTower

Capt'n Midnight wrote: »

Average waiting time is 37.8 weeks

:eek:

LeixlipRed wrote: »

This thread is almost 5 years old. Any real need to repopen it??

Capt'n Midnight

http://www.drivingtest.ie/drivingtest/EnglishStats.pdf

pass rate isn't vastly better than before, still the waiting time has gone down

42.5 % in Rathgar and 64.1 % in Ballina
why are the test rates so different in other places

                                 Currently Scheduling Car Applications
       Pass Rate 2008   %                Received on this date....
Athlone                54.5 Athlone                           29/09/2009
Ballina                64.1 Ballina                           30/09/2009
                       56.5 Birr
Birr                                                          28/09/2009
Buncrana               60.1 Buncrana                          06/10/2009
Carlow                 62.5 Carlow                            06/10/2009
Carrick-on-Shannon     57.4 Carrick-on-Shannon                23/09/2009
                       59.9 Castlebar
Castlebar                                                     29/09/2009
Cavan                  52.4 Cavan                             26/09/2009
Churchtown             59.2 Churchtown                        25/09/2009
Clifden                60.1 Clifden                           29/10/2009
Clonmel                50.4 Clonmel                           13/10/2009
                       61.1 Cork
Cork                                                          21/09/2009
                       59.8 Donegal
Donegal                                                       25/09/2009
Dundalk                57.0 Dundalk                           17/09/2009
                       56.3 Dungarvan
Dungarvan                                                     05/10/2009
Ennis                  60.5 Ennis                             01/10/2009
                       54.7 Finglas
Finglas                                                       13/10/2009
                       62.9 Galway
Galway                                                        08/10/2009
                       59.0 Gorey
Gorey                                                         24/09/2009
                       54.9 Kilkenny
Kilkenny                                                      12/10/2009
                       57.8 Killarney
Killarney                                                     05/10/2009
Kilrush                52.5 Kilrush                           15/09/2009
                       60.7 Letterkenny
Letterkenny                                                   20/09/2009
Limerick               60.4 Limerick                          15/10/2009
                       58.6 Longford
Longford                                                      30/09/2009
                       52.5 Loughrea
Loughrea                                                      24/09/2009
Mallow                 52.9 Mallow                            22/09/2009
Monaghan               63.3 Monaghan                          12/09/2009
                       51.8 Mullingar
Mullingar                                                     12/10/2009
Naas                   60.3 Naas                              08/10/2009
Navan                  58.1 Navan                             30/09/2009
                       69.1 Nenagh
Nenagh                                                        14/10/2009
Newcastle West         59.9 Newcastle West                    16/10/2009
Portlaoise             60.4 Portlaoise                        13/10/2009
                       57.7 Raheny
Raheny                                                        30/09/2009
                       42.5 Rathgar
Rathgar                                                       09/09/2009
Roscommon              59.8 Roscommon                         18/09/2009
Shannon                56.1 Shannon                           26/09/2009
Skibbereen             55.4 Skibbereen                        04/10/2009
                       62.5 Sligo
Sligo                                                         10/09/2009
                       59.2 Tallaght
Tallaght                                                      09/09/2009
Thurles                48.2 Thurles                           02/10/2009
                       45.0 Tipperary
Tipperary                                                     12/10/2009
Tralee                 54.7 Tralee                            12/10/2009
Tuam                   56.2 Tuam                              29/09/2009
Tullamore              49.8 Tullamore                         08/10/2009
Waterford              53.7 Waterford                         12/10/200code]
Wexford                45.8 Wexford                           05/10/2009
Wicklow                55.5 Wicklow                           21/09/2009
Overall Total         57.2%

RoundTower

I've been doing my bit to keep the pass rate in Rathgar down. So would I be better taking my next test somewhere else or are the different pass rates a reflection of the different populations taking the test?