(a)[3]
For size $A$ stones, the masses have standard deviation $6$ grams. The mean mass of a random sample of $200$ size $A$ stones is $45$ grams. Find a $95\%$ confidence interval for the population mean mass of size $A$ stones.
(b)[4]
For size $B$ stones, the masses have standard deviation $11$ grams. From a random sample of size $200$, an $\alpha\%$ confidence interval for the population mean mass is obtained with width $4$ grams. Find $\alpha$.