SOLUTION: it is assumed that labour productivity of particular members in a factory can be described by a normal distribution with sigma=3.what is probability that a sample mean calculated f

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Question 234924: it is assumed that labour productivity of particular members in a factory can be described by a normal distribution with sigma=3.what is probability that a sample mean calculated for 9 randomly chosen workers differs from the population mean by more than 2 units?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
it is assumed that labour productivity of particular members in a factory can be described by a normal distribution with sigma=3.what is probability that a sample mean calculated for 9 randomly chosen workers differs from the population mean by more than 2 units?
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The std of the sample means is 3/sqrt(3).
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Comment: You did not post a mean value for the population
and I made the mistake of assuming it was 3. All the
work I did is based on that assumption.
Check your problem statement. Maybe that phrase
"more that 2 units" refers to standard deviation
units.
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If x-bar differs from the mean by more that 2 units,
x-bar is less than 1 or x-bar is greater than 5.
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z(1) = (1-3)/sqrt(9) = -2/3
z(5) = (5-3)/sqrt(9) = 2/3
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P(x-bar < 1)= P(z < -2/3) = 0.2525
P(x-bar > 4)= P(z > 2/3) = 0.2525
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Ans: 0.2525+0.2525 = 0.5050
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Cheers,
Stan H.