The masses of sweets produced by a machine are normally distributed with mean $\mu $ grams and standard deviation 1.0 grams. A random sample of 65 sweets produced by the machine has a mean mass of 29.6 grams.
a) Find a 99% confidence interval for $\mu $.
The manufacturer claims that the machine produces sweets with a mean mass of 30 grams.
b) Use the confidence interval found in part (a) to draw a conclusion about this claim.
c) Another random sample of 65 sweets produced by the machine istaken. This sample gives a 99% confidence interval that leads to a different conclusion from that found in part (b). Assuming that the value of $\mu $ has not changed, explain how this can be possible.
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