Question 1081734: A simple random sample of size n=15 is obtained from a population with μ=66 and σ=14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of overbarx.
(b) Assuming the normal model can be used, determine P(overbar x < 69.5).
(c) Assuming the normal model can be used, determine P(overbar x ≥ 67.6).
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 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
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