Question 1077156: Question 1:
Suppose a simple random sample of size n=10 is obtained from a population with
μ=67 and σ=19
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution
(b) Assuming the normal model can be used, determine
P(x (the x has an overbar over it) <70.3).
(c) Assuming the normal model can be used, determine
P(x (the x has an overbar over it) ≥68.7).
I know that the population must be normally distributed and that the sampling distribution is μx = 67and
Σx=19/the square root of 10.
However, I do not know what the answer to B and C are.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z<(x-mean)/s/sqrt (n)
z<3.3*sqrt(10)/19=0.5492
P=0.7086
It is a z test with s/sqrt(n) in the denominator.
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z>(68.7-67)/19/sqrt (10)
z>(1.7)*sqrt(10)/19=0.2819
P=0.3886
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