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 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.