Question 1138520
Population should be normally distributed.  Or, samples that are large enough will tend to have a normal distribution should the population distribution not be too skewed.  The more skew, the larger the sample sizes need to be.

The sampling distribution of the sample mean is the population mean with variance sigma/ sqrt (n), where n is the sample size

z=(x bar-mean)/sigma/sqrt (n)
<(70.4-66)/16/sqrt(12)
<4.4*sqrt(12)/16=0.95
that probability is 0.8289

>(67.7-66)/16/sqrt(12)
>0.37
That probability is 0.3557