A factory produces packets of cereal. The weight of cereal in each packet, W W\,W g, is normally distributed with mean 400 g. Given that 20% of packets contain more than 405 g.
Find the value of k k\,k such that P(k<W<410)=0.50P(k < W < 410) = 0.50P(k<W<410)=0.50.
The production process is adjusted so that the standard deviation of the weight of cereal is now 6 g. Following the adjustments, the quality control manager believes that the mean weight of cereal in each packet is less than 400 g. She takes a random sample of 25 packets and finds the mean weight to be 397.5 g. Test the manager's belief at the 5% significance level. You should state your hypotheses clearly.
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.