A machine is designed to fill bags of sugar with a target mean weight of 500 g. The weight of sugar in a bag is normally distributed. A quality control manager suspects the machine is underfilling the bags. The weights, xxx g, of 10 randomly selected bags are recorded, and the following statistics are calculated:
xˉ=492.5s=9.24 \bar{x} = 492.5 \quad s = 9.24 xˉ=492.5s=9.24Stating your hypotheses clearly, test at the 5% significance level whether or not the manager's suspicion is supported.
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.