6 The weight, \(X\) kilograms, of sand in a bag can be modelled by a normal random variable with unknown mean \(\mu\) and known standard deviation 0.4 .
- The sand in each of a random sample of 25 bags from a large batch is weighed. The total weight of sand in these 25 bags is found to be 497.5 kg .
- Construct a 98\% confidence interval for the mean weight of sand in bags in the batch.
- Hence comment on the claim that bags in the batch contain an average of 20 kg of sand.
- State why use of the Central Limit Theorem is not required in answering part (a)(i).
- The weight, \(Y\) kilograms, of cement in a bag can be modelled by a normal random variable with mean 25.25 and standard deviation 0.35.
A firm purchases 10 such bags. These bags may be considered to be a random sample.
- Determine the probability that the mean weight of cement in the 10 bags is less than 25 kg .
- Calculate the probability that the weight of cement in each of the 10 bags is more than 25 kg .
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