A new technology for the production of integrated circuits is being mastered. The technology will be rejected if the percentage of the defective integrated circuits exceeds 2%. How many integrated circuits have to be checked to make sure that the technology gives a sufficiently small amount of defects with a probability of 0.5% if the actual probability is p = 0.04? Use a = 0.05. Use the z-values rounded to two decimal places to obtain the answer. n = the absolute tolerance is + / -1

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Mathematics

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A new technology for the production of integrated circuits is being mastered. The technology will be rejected if the percentage of the defective integrated circuits exceeds 2%. How many integrated circuits have to be checked to make sure that the technology gives a sufficiently small amount of defects with a probability of 0.5% if the actual probability is p = 0.04? Use a = 0.05. Use the z-values rounded to two decimal places to obtain the answer. n = the absolute tolerance is + / -1

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Natalya Leach · Answer 1

5901

Step-by-step explanation:

The margin of error is the critical value times the standard error.

ME = CV * SE

For α = 0.05, the critical value is z = 1.96.

The standard error of a proportion is √ (pq/n). Given p = 0.04, then q = 1-p = 0.96.

The margin of error is 0.5% or 0.005.

Plugging in:

0.005 = 1.96 √ (0.04 * 0.96 / n)

n ≈ 5901