A quality control engineer at a semiconductor factory monitors the production of high-performance microchips. The probability that any individual microchip is defective is 0.12.
Suggest a suitable distribution to model the number of defective microchips identified in a batch of n n\,n microchips.
In a specific sample of 15 microchips, find the probability that at least 4 are defective.
Determine the minimum number of microchips that must be sampled such that the probability of finding at least one defective chip is greater than 0.95.
The factory also operates a specialized production line where the probability of a chip being 'premium grade' is 0.25. On this line, 200 chips are produced every hour. Using a suitable approximation, find the probability that more than 60 chips are identified as 'premium grade' in a randomly chosen hour.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.