Question 1138520: A simple random sample of size nequals12 is obtained from a population with muequals66 and sigmaequals16.
(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 x overbar.
(b) Assuming the normal model can be used, determine P(x overbarless than70.4).
(c) Assuming the normal model can be used, determine P(x overbargreater than or equals67.7).
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 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
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