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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.