What happens in Prob. 1 if the sample size is increased to 50? First guess. Then calculate. Graph the OC curve and compare.

Data from Prob. 1

Lots of kitchen knives are inspected by a sampling plan that uses a sample of size 20 and the acceptance number c = 1. What is the probability of accepting a lot with 1%, 2%, 10% defectives (knives with dull blades)? Use Table A6 of the Poisson distribution. Graph the OC curve.

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Probability function f(x) [see (5), Sec. 24.7] and distribution function F(x) A- 0.2 Fx) A- 0.3 A- 0.1 H- 04 fx) F(x) fu) F(x) f) Fx) х 0. 0. 0. 0. 9048 0.9048 8187 0.8187 7408 0.7408 6703 0.6703 6065 0.6065 0.9825 0905 0.9953 1637 2222 0.9631 2681 0.9384 3033 0.9098 0.9908 0.9964 0.9856 2 0045 0164 0.9989 0333 0536 0.9921 0758 0002 1,0000 0011 0001 0.9999 0033 0.9997 0072 0.9992 0126 0.9982 0.9998 4 0000 1.0000 1.0000 0003 1.0000 0007 0.9999 0016 1.0000 0001 0002 1.0000 H - 0.8 F(x) A- 0.6 A- 0.7 F(x) A- 0.9 fx) F(x) f) F(x) х 0. 0. 0. 0. 5488 05488 4966 0.4966 4493 0.4493 4066 0.4066 3679 0.3679 0.8442 0.7725 3293 0.8781 3476 3595 0.8088 3659 3679 0.7358 0.9526 0.9197 0.98 10 0988 0.9769 1217 0.9659 1438 1647 0.9371 1839 0198 0.9966 0.9996 0284 0.9942 0383 0.9909 0494 0.9865 0613 0.9977 0030 0050 0.9992 0077 0.9986 0111 0153 0.9963 0.9994 0004 1.0000 0007 0.9999 0012 0.9998 0020 0.9997 0031 0001 0003 1.0000 0002 1.0000 1.0000 0005 0.9999 0001 1.0000 4 fx) fx) Fx) F(x) fx) F(x) F(x) х 0. 0. 0. 0. 0. 0.0183 2231 0.2231 1353 0.1353 0498 0.0498 0183 0067 0.0067 0337 0842 3347 0.578 2707 0.4060 1494 2240 0.1991 0733 0.0916 0.0404 0.8088 0.2381 0.4335 0.6288 2 2510 2707 0.6767 0.4232 1465 0.1247 0.2650 1804 0902 0361 1954 1255 0.9344 0.8571 2240 0.6472 1404 0.9473 0.9834 1680 1008 1755 1755 0471 0141 0.9814 0.8153 1954 0.4405 0.9955 0.6160 0.9161 1563 0.7851 0.7622 0035 0.9991 0120 0.9955 0504 0.9665 1042 0.8893 1462 0.9989 0595 0008 0.9998 0034 0216 0.9881 0.9489 1044 0.8666 1.0000 0001 0009 0.9998 0081 0.9962 0298 0.9786 0653 0.9319 0002 0132 0053 1.0000 0027 0.9989 0.9919 0363 0.9682 0.9863 0.9997 10 0008 0.9972 0181 11 0002 0.9999 0019 0.9991 0082 0.9945 1,0000 0006 0.9997 0.9980 12 0001 0034 13 0002 0.9999 0013 0.9993 14 0001 1.0000 0005 0.9998 15 0002 0.9999 1.0000 16 0000