Basic Statistics20795 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 (i) at least 12 will have thick enough coatings, (ii) at most 2 will have thick enough coatings, and (ii) exactly 10 w
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 (i) at least 12 will have thick enough coatings, (ii) at most 2 will have thick enough coatings, and (ii) exactly 10 will have thick enough coatings. [5]
- Probability a chip receives thick enough coating: $p = 0.70$ - Failure probability: $q = 1 - p = 0.30$ - Number of chips: $n = 15$ - $X$ = number of chips with thick enough coating $\sim \text{Binomial}(15, 0.70)$ Formula: $$P(X = k) = \binom{15}{k}(0.70)^k (0.30)^{15-k}$$