The operating life, LLL hours, of a specialized 'X-7' industrial diode is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Quality control testing reveals that 10%10\%10% of the diodes fail before reaching 800800800 hours of operation, while 20%20\%20% of the diodes exceed a lifespan of 120012001200 hours.
Determine the value of μ\muμ and the value of σ\sigmaσ.
(i) State the value of P(L≠1000)P(L \neq 1000)P(L=1000). (ii) Find P(L<1000)P(L < 1000)P(L<1000).
These diodes are sold in batches of 121212. Calculate the probability that, in a randomly selected batch, no more than 333 diodes have an operating life of less than 100010001000 hours. You may assume that the lifespans of the diodes are independent.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.