The daily consumption of water by households in a specific region, WWW, is modelled by a normal distribution with mean 420 litres and standard deviation 64 litres.
State the probability that the water consumption of a randomly selected household on a given day is not equal to 420 litres.
Environmental policies were introduced to encourage water conservation. Following these changes, a random sample of 36 households was monitored. The total water consumption for this group over a single day was found to be 13,824 13,824\,13,824 litres.
It is assumed that the distribution of daily water consumption remains normal with a standard deviation of 64 litres.
Investigate, at the 10% level of significance, whether the mean daily water consumption has changed.
A local official argues that if a different sample of 36 households had been selected, the conclusion of the hypothesis test in part (b) would definitely be the same. Comment on the validity of this claim.
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.