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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.