The lifespan of a high-performance laser diode, DDD hours, is normally distributed with mean μ\muμ and standard deviation 120120120. It is known that 2%2\%2% of these diodes fail in less than 4500 hours4500\text{ hours}4500 hours, find:
the value of μ\muμ to two decimal places.
the percentage of diodes that last longer than 5000 hours5000\text{ hours}5000 hours.
The manufacturing process is updated such that the lifespan of the diodes is normally distributed with mean 480048004800 and standard deviation σ\sigmaσ.
Given that 98%98\%98% of diodes now last between 4650 hours4650\text{ hours}4650 hours and 4950 hours4950\text{ hours}4950 hours, find the value of σ\sigmaσ.
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.