SOLUTION: A random sample of 100 items is selected from a population of size 350. What is the probability that the sample mean will exceed 199 if the population mean is 195 and

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Question 1059212: A random sample of
100
items is selected from a population of size
350.
What is the probability that the sample mean will exceed
199
if the population mean is
195
and the population standard deviation equals
25?
Hint: Use the finite population correction factor since the sample size is more than; 5% of the population size.)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A random sample of 100items is selected from a population of size 350.
What is the probability that the sample mean will exceed 199
if the population mean is 195and the population standard deviation equals 25?
Hint: Use the finite population correction factor since the sample size is more than; 5% of the population size.)
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fpc = sqrt[(N-n)/(N-1)]
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z(199) = (199-195)/fpc = [4/sqrt(25)][sqrt[(350-100)/(350-1)] = 0.9452
P(x-bar > 199) = P(z > 0.9452) = normalcdf(0.9452,100) = 0.1723
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Cheers,
Stan H.
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