Bionomail Probablity (1 Viewer)

[Shady01]

Help! lol if you guys get a sec

In order to form an estimate of the quality of mass-produced articles, a customer adopts the following double sampling scheme. A random sample of 10 is inspected; if no defectives are found, he accepts the lot; if 4 or more defectives are found, he rejects the lot; but if 1,2 or 3 defectives are found, he takes a second sample of 10 and if the total of defectives in the two samples is 4 or more, he rejects the lot, but otherwise accepts the lot. Calculate the probability that the lot which is known to be 10 per cent defective is accepted.

 

[Trev]

Hehe bionomail.

 

[JulieClark]

Chance of 1 item being defective = <?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" oreferrelative="t" o:spt="75" coordsize="21600,21600"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><vath o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></vath><?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 15.75pt; HEIGHT: 30.75pt" ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\Vanessa\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></v:imagedata></v:shape>
P(0 defective in a sample of 10)=<v:shape id=_x0000_i1026 style="WIDTH: 86.25pt; HEIGHT: 36.75pt" ole="" type="#_x0000_t75"> <v:imagedata o:title="" src="file:///C:\DOCUME~1\Vanessa\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz"></v:imagedata></v:shape>
<o> </o>
P(1 defective)= <v:shape id=_x0000_i1027 style="WIDTH: 80.25pt; HEIGHT: 36.75pt" ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\Vanessa\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz"></v:imagedata></v:shape>
<o> </o>
P(2 defective)= <v:shape id=_x0000_i1028 style="WIDTH: 83.25pt; HEIGHT: 36.75pt" ole="" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\Vanessa\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz"></v:imagedata></v:shape>
<o> </o>

 

[JulieClark]

arrgh! well, thats what happens when you try and paste maths type stuff heere. oh wel, sorry about that, but i did it by finding the probablity of getting zero, one two and three defectives and determing that:
P(accepted) = P(0) + P(1) x (P(0) + P(1) + P(2)) + P(2) x ((P(0) + P(1)) + P(3) x P(0)

(As all other combinations result in it not being accepted)

= 87.15% using a calculator

 

[Shady01]

shit yr smart cheers thanx fer that