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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.