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.
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.