The volume of orange juice in a bottle produced by a filling machine is normally distributed with a mean of 505 ml and a standard deviation of 4.2 ml.
Find the probability that a randomly selected bottle has a volume of less than 498 ml.
The production manager suspects that the mean volume of juice in the bottles is lower than the specified 505 ml.
Write down the null and alternative hypotheses for the manager's suspicion.
A random sample of 25 bottles is taken and the mean volume is found to be 503 ml.
Carry out a test at the 5% significance level to see if there is evidence that the mean volume is less than 505 ml.