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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
