How will the probabilities in Prob. 1 with n = 20 change (up or down) if we decrease c to zero? First guess.

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.

Probability function f(x) [see (5), Sec. 24.7] and distribution function F(x) H-0.1 -0.2 -0.3 f(x) F(x) -0.4 f(x) F(x) f(x) F(x) 0. 0. 9048 0. 7408 0.7408 6703 X 0 1234 5 X 12345 H-0.6 f(x) F(x) 0. 0 5488 6 7 x 12345 -15 f(x) F(x) 0. 0 2231 0.2231 67699 0.9048 10 3347 0.5578 2510 0.8088 1255 0.9344 4 0471 0.9814 0141 0.9955 11 12 0035 0.9991 0008 0.9998 8 0001 1.0000 15 16 0905 0.9953 1637 0045 0.9998 0164 0011 0.9999 0.5488 3293 0.8781 0988 0.9769 0198 0.9966 00:30 0.9996 0004 1.0000 f(x) 0. 8187 0002 1.0000 0033 0000 1.0000 0001 1.0000 0003 f(x) F(x) 0. 4966 0.8187 #4 -0.7 0.9825 0.9989 0333 f(x) 0. 1353 1804 0902 0361 F(x) 4-2 2222 0.9631 0.9964 3476 1217 0284 0.9942 0383 00:50 0.9992 0077 0007 0.9999 0012 0001 1.0000 0002 0.1353 2707 0.4060 0.6767 0.8571 H-0.8 0.4966 0.8442 3595 0.8088 0.9659 1438 0.9997 1.0000 f(x) 0. 4493 0.4493 4066 F(x) f(x) 0. 0498 H-3 0.9473 0.9834 1008 1.0000 0.0498 1494 0.1991 2240 0.4232 2240 0.6472 2681 0536 0.6703 0.9384 3033 0.9921 0758 0072 0.9992 0126 0007 0.9999 0016 0001 1.0000 0002 1680 0.8153 0.9161 H-0.9 F(x) 0.4066 0.7725 3659 0.9526 1647 0.9371 0.9909 0494 0.9986 0111 0.9977 0153 0.9998 0020 0.9997 0031 0.9865 0613 0003 f(x) F(x) f(x) 0.9665 1042 0120 0.9955 0504 0034 0.9989 0216 0.9881 0595 0009 0.9998 0081 0.9962 1.0000 0027 0.9989 0002 0008 0.9997 0053 -0.5 f(x) F(x) 0. 6065 4 F(x) 1.0000 0005 0001 0002 0.9999 0019 0001 1.0000 0006 0002 H-1 f(x) F(x) 0. 3679 0132 0.9919 0.9972 0.3679 3679 0.7358 1839 0.9197 0.98 10 0.9963 0.9994 f(x) 0. 0067 0.8893 1462 0.9489 1044 0298 0.9786 0653 0363 0181 H-5 0183 0.0183 0733 0.0916 0337 0.0404 1465 0.2381 0842 0.1247 1954 0.4335 1404 0.2650 1954 0.6288 1563 0.7851 0.6065 0.9098 0.9856 0.9982 0.9998 1.0000 1755 1755 0.9991 0082 0.9997 0034 0.9999 0013 0001 1.0000 0005 0.9999 1.0000 0000 F(x) 0.0067 0.4405 0.6160 0.7622 0.8666 0.9319 0.9682 0.9863 0.9945 0.9980 0.9993 0.9998 0002 0.9999 1.0000