Question 1081734
the population must be treated as normally distributed or close to it, given that a sample is being taken that is relatively small.
the sampling distribution is then N~(66, 14/sqrt(10))
probability mean is  < 69.5 in the sample is z<(69.5-66)/(14/sqrt(10))
=3.5*sqrt(10)/14=0.7906
probability z < 0.79 is 0.7852
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z>=(67.6-66)*sqrt(10)/14
z>0.36
probability is 0.3594