In: Statistics and Probability
a factory creating widgets tests samples of it’s products to see if they meet quality standards.suppose that in each batch of 10000 widgets, the factory tests 200 widgets. if more than 12 of that sample did not meet the standard, the batch is rejected. suppose we know that a certain batch of widgets has 850 faulty widgets. what is the probability that the factory would not reject the batch?
Probability of faulty widgets = 850/10000
=0.085
X | P(X) | |
P ( X = 0) = C (200,0) * 0.085^0 * ( 1 - 0.085)^200= | 0 | 0.0000 |
P ( X = 1) = C (200,1) * 0.085^1 * ( 1 - 0.085)^199= | 1 | 0.0000 |
P ( X = 2) = C (200,2) * 0.085^2 * ( 1 - 0.085)^198= | 2 | 0.0000 |
P ( X = 3) = C (200,3) * 0.085^3 * ( 1 - 0.085)^197= | 3 | 0.0000 |
P ( X = 4) = C (200,4) * 0.085^4 * ( 1 - 0.085)^196= | 4 | 0.0001 |
P ( X = 5) = C (200,5) * 0.085^5 * ( 1 - 0.085)^195= | 5 | 0.0003 |
P ( X = 6) = C (200,6) * 0.085^6 * ( 1 - 0.085)^194= | 6 | 0.0010 |
P ( X = 7) = C (200,7) * 0.085^7 * ( 1 - 0.085)^193= | 7 | 0.0026 |
P ( X = 8) = C (200,8) * 0.085^8 * ( 1 - 0.085)^192= | 8 | 0.0059 |
P ( X = 9) = C (200,9) * 0.085^9 * ( 1 - 0.085)^191= | 9 | 0.0117 |
P ( X = 10) = C (200,10) * 0.085^10 * ( 1 - 0.085)^190= | 10 | 0.0207 |
P ( X = 11) = C (200,11) * 0.085^11 * ( 1 - 0.085)^189= | 11 | 0.0332 |
P ( X = 12) = C (200,12) * 0.085^12 * ( 1 - 0.085)^188= | 12 | 0.0485 |
P(X<=12)
= 0.1240
probability that the factory would not reject the batch =0.124
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