A lightbulb manufacturer claims that only 2%2\%2% of its LED bulbs are defective. To investigate this claim, a quality control manager selects a random sample of 150150150 bulbs and finds that 888 are defective.
Use a suitable approximation to test, at the 5%5\%5% level of significance, whether the manufacturer is understating the proportion of defective bulbs. 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.