Quality control engineers at a semiconductor plant monitor microchips for a specific manufacturing defect. Historical data indicates that the probability of a microchip possessing this defect is 0.012.
Define a suitable model for the distribution of the number of microchips possessing this defect in a batch of nnn chips.
State one modeling assumption required for the distribution in part (a) to be valid.
Using a suitable approximation, determine the probability that exactly 5 out of a batch of 250 microchips are found to have this defect.
Justify the use of the approximation chosen in part (c).
A manufacturer claims that 65% of their solar panels exceed an efficiency rating of 22%.
From a random sample of 180 panels, 104 are found to exceed this rating.
Using a suitable approximation, test the manufacturer's claim at the 5% level of significance. State your hypotheses clearly.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.