The operational endurance of a random sample of 15 'Volt-X' industrial sensors is measured under standard load. The mean endurance of the sample is recorded as 118.4 hours118.4\text{ hours}118.4 hours. The endurance times of these sensors are known to follow a normal distribution.
Given that the population standard deviation for these sensors is 4.2 hours4.2\text{ hours}4.2 hours,
estimate the limits between which 95%95\%95% of the endurance times of individual sensors lie.
find a 98%98\%98% confidence interval for the mean endurance time of the 'Volt-X' sensors.
A quality control engineer claims that the true mean endurance time of these sensors is 121.5 hours121.5\text{ hours}121.5 hours.
Comment on the engineer's claim. Give a reason for your answer.
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.