SOLUTION: A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this popula

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Question 975679: A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:
Select one:
a. 0.0166. Incorrect
b. 0.0228.
c. 0.3708.
d. 0.0394.

Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:
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z(56) = (56-60)/[10/sqrt(25)] = -4/2 = -2
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P(x-bar < 56) = P(z < -2) = normalcdf(-100,-2) = 0.0228
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Cheers,
Stan H.
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Select one:
a. 0.0166.
b. 0.0228.
c. 0.3708.
d. 0.0394.

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=x bar-mean/sd/sart (n)
z<= (56-60)/10/sqrt(25)
<= -4 /2 z=<-2
probability is 0.0228
B.