The lifespans of high-performance LED modules tested under extreme thermal stress are recorded. A random sample of 15 modules yields a mean lifespan of 1250 hours1250\text{ hours}1250 hours. The lifespans are known to follow a normal distribution with a population standard deviation of 45 hours45\text{ hours}45 hours.
Estimate the bounds within which 90%90\%90% of the lifespans of individual modules are expected to fall.
Construct a 95%95\%95% confidence interval for the population mean lifespan μ\muμ of these modules.
An engineer asserts that the true mean lifespan of these modules under these conditions is 1280 hours1280\text{ hours}1280 hours.
Evaluate the engineer's assertion based on your result in part (b). Provide a mathematical justification.
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.
