The volume of orange juice in a carton produced by a bottling machine is normally distributed with a mean of 252 ml and a standard deviation of 3.5 ml.
Find the probability that a randomly selected carton of orange juice contains less than 245 ml.
Write down the null and alternative hypotheses to test if the mean volume is lower than 252 ml.
A sample of 30 cartons is taken and the mean volume is found to be 251 ml. Carry out a test at the 5% significance level to see if there is evidence that the machine is producing cartons with a mean of less than 252 ml.
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.