- A machine fills jars with jam. The weight of jam in each jar is normally distributed. To check the machine is working properly the contents of a random sample of 15 jars are weighed in grams. Unbiased estimates of the mean and variance are obtained as
$$\hat { \mu } = 560 \quad s ^ { 2 } = 25.2$$
Calculate a 95\% confidence interval for,
- the mean weight of jam,
- the variance of the weight of jam.
A weight of more than 565 g is regarded as too high and suggests the machine is not working properly.
- Use appropriate confidence limits from parts (a) and (b) to find the highest estimate of the proportion of jars that weigh too much.