6 A garden centre sells bags of stones and large bags of gravel.
The weight, \(X\) kilograms, of stones in a bag can be modelled by a normal distribution with unknown mean \(\mu\) and known standard deviation 0.4
The stones in each of a random sample of 36 bags from a large batch is weighed. The total weight of stones in these 36 bags is found to be 806.4 kg
- Find a 98\% confidence interval for the mean weight of stones in the batch.
- Explain why the use of the Central Limit theorem is not required to answer part (a)
The manufacturer of these bags of stones claims that bags in this batch have a mean weight of 22.5 kg
- Using your answer to part (a), comment on the claim made by the manufacturer.
The weight, \(Y\) kilograms, of gravel in a large bag can be modelled by a normal distribution with mean 850 kg and standard deviation 5 kg
A builder purchases 10 large bags of gravel.
- Find the probability that the mean weight of gravel in the 10 large bags is less than 848 kg