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.
