Question 1003683
To calculate a confidence interval we need the confidence level, statistic, and margin of error.
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a) margin of error = critical value * standard deviation of statistic
we want the 99% confidence interval on the population mean, 
note that we use the t-distribution because our sample size is < 30
the degrees of freedom(df) = 22 - 1 = 21
t(alpha/2) is determined by consulting the t-distribution table
t(alpha/2) for 99% cf is 2.831
99% cf for population mean = 60 + or - (t(alpha/2) * (10/sqrt(22)) =
60 + or - (2.831 * 2.13) = 60 + or - 6.03
our 99% cf is (53.97, 66.03)
note that the sample mean is also the population mean
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b) the std dev of the sample = st dev of population / sqrt(sample size)
for this part of the problem
std dev of the population = 10 * sqrt(22) = 46.9
99% cf for population mean = 60 + or - 2.831 * (46.9/sqrt(22)) =
60 + or - 28.3 = (31.7, 88.3)