In a manufacturing facility for precision sensors, the probability of a sensor having a calibration error is p=0.12p = 0.12p=0.12. Errors occur independently in each sensor.
Find the probability that in a random sample of 25 sensors, there will be
(i) exactly 4 sensors with a calibration error,
(ii) at least 6 sensors with a calibration error.
In a large batch of 600 sensors, use a suitable approximation to find the probability that the number of sensors with calibration errors is more than 80.
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.