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.
284 exam-style questions on CCEA A Level Maths 4.5 Statistical distributions (A-level only), covering 4.5.1 Statistical distributions (A-level only) and 4.5.2 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.