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.
147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.