The lifetime of an electronic component, in hours, is modelled by a normal distribution with mean 1200 hours and standard deviation 150 hours.
Write down the two lifetimes at which the graph of the probability density function has its points of inflection.
Find the probability that a randomly chosen component lasts longer than 1400 hours. Give your answer to 3 significant figures.
Find the lifetime that is exceeded by 90% of these components. Give your answer to 3 significant figures.
A new batch of 30 components is tested. The total lifetime of the 30 components is 34 800 34\,800\,34800 hours. Stating your hypotheses clearly, test at the 10% significance level whether the mean lifetime of components in the new batch has decreased. You may assume that the lifetimes are still normally distributed with standard deviation 150 hours.
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.