A team of engineers tests the operational lifespan of a new emergency beacon under sub-zero temperatures. A random sample of 12 beacons is activated, and the time until failure, ttt hours, is recorded. The data are summarized as follows:
∑t=504,∑t2=21450 \sum t = 504, \quad \sum t^2 = 21450 ∑t=504,∑t2=21450You may assume that the lifespans are normally distributed.
Calculate a 98% confidence interval for: (i) the mean lifespan of the beacons, (ii) the variance of the lifespan of the beacons.
Beacons that fail in less than 40 hours are designated as "short-life". Using the relevant confidence limits from part (a), determine the lowest estimate for the proportion of beacons that are short-life.
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.