An electronics engineer measures the resistance, rrr ohms, of a specific component. The measured resistance, XXX ohms, is normally distributed with mean rrr ohms and standard deviation 0.80.80.8 ohms.
Find the probability that XXX is within 1.01.01.0 ohm of rrr.
The same component is measured 25 times and the results are recorded.
Find the probability that the sample mean of these 25 results, Xˉ\bar{X}Xˉ, is within 0.40.40.4 ohms of rrr.
Given that the mean of these 25 measurements is 120.4120.4120.4 ohms, find a 95%95\%95% confidence interval for rrr.
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.