Question

during one stage in manufacturing of integrated circuit chips a coating must be applied if 70% of chips received a thick enough coating find the probability that among. 1)at least 12. 2)at most 6. 3) exactly 10​

Answer 1

Given : during one stage in manufacturing of integrated circuit chips a coating must be applied 70% of chips received a thick enough coating

To Find :  probability that among  15 chips

. 1)at least 12.

2)at most 6.

3) exactly 10​

Solution:

p = 0.7

q = 1 - p = 1 - 0.7 = 0.3

n = 15

P(x) = ⁿCₓpˣqⁿ⁻ˣ

at least 12.

= P(12) + P(13) + P(14) + P(15)

= ¹⁵C₁₂(0.7)¹²(0.3)³    +  ¹⁵C₁₃(0.7)¹³(0.3)² + ¹⁵C₁₄(0.7)¹⁴(0.3)¹    +  ¹⁵C₁₅(0.7)¹⁵(0.3)²⁰

2)at most 6

= P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

Exactly 10

P(10) =  ¹⁵C₁₀(0.7)¹⁰(0.3)⁵

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