The lifespan, T T\,T hours, of a certain component is normally distributed. Given that P(T<800)=0.3P(T < 800) = 0.3P(T<800)=0.3 and P(T>1200)=0.15P(T > 1200) = 0.15P(T>1200)=0.15.
Find the mean and standard deviation of the lifespan of the component.
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.