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  A random sample of size n = 64 is taken and the sample mean $\bar{X}$ is computed. Assume the population mean is $\mu$ = 120 and the population standard deviation is $\sigma$ = 16.

(a) Find the mean and standard deviation of $\bar{X}$.

(b) Find approximately $P[\bar{X} < 118]$. What major theorem are you using?