Basic Statistics20785 marksNumerical: binomial distribution probabilityBinomial distribution
During one stage in the manufacture of integrated circuit chips, a coating must be applied. If 70% of chips received a thick enough Coating. find the probability that among 15 chips (1) at least 12 will have thick enough coatings, and (2) exactly 10 will have thick enough coatings.
During one stage in the manufacture of integrated circuit chips, a coating must be applied. If 70% of chips received a thick enough Coating. find the probability that among 15 chips (1) at least 12 will have thick enough coatings, and (2) exactly 10 will have thick enough coatings. [5]
- Probability of thick enough coating: $p = 0.70$ - Probability of not thick enough: $q = 1 - p = 0.30$ - Sample size: $n = 15$ Binomial distribution: $P(X = r) = \binom{n}{r} p^r q^{n-r}$ --- $$P(X \geq 12) = P(12) + P(13) + P(14) + P(15)$$ P(X = 12): $$\binom{15}{12}(0.7)^{12}(0.3)^{3} = 455 \t...