Question 9A: Probability and Statistics

A factory manufactures aluminium rods. One of its machines can be set to produce rods of a specified length. The lengths of these rods are normally distributed, with mean equal to the specified length and standard deviation equal to 0·2 mm.

The machine has been set to produce rods of length 40 mm.

What is the probability that a randomly selected rod will be less than 39·7mm in length?

The operators want to check whether the setting on the machine is still accurate.

They take a random sample of 10 rods and measure their lengths. The lengths in millimetres are:

39·5 40·0 39·7 40·2 39·8

39·7 40·2 39·9 40·1 39·6

Conduct a hypothesis test at the 5 per cent level of significance to decide whether the machine’s setting has become inaccurate.

You should start by clearly stating the null hypothesis and the alternative hypothesis, and finish by clearly stating what you conclude about the machine.