Question 415757: Geological engineers are very important people and sometimes work closely with civil
engineers. In bridge construction, geological engineers conduct water-level surveys to
measure how level the concrete slabs are. They usually take these measures at eight
different spots on the slab. We are interested in the maximum differential between
these spots. Data was collected for over 2300 concrete slabs. The maximum
differential, x, had a mean of µ=0.64 inch and a standard deviation of = 0.176 inch.
Consider a sample of n=400 slabs selected from those surveyed and let ̅ represent the
mean of the sample. These slabs were selected without replacement from the total of 2300
slabs collected.
a. Find E (X) and Var(X)
b. Find P(X>.63)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! We are interested in the maximum differential between
these spots. Data was collected for over 2300 concrete slabs. The maximum
differential, x, had a mean of µ=0.64 inch and a standard deviation of = 0.176 inch.
Consider a sample of n=400 slabs selected from those surveyed and let X-bar represent the
mean of the sample. These slabs were selected without replacement from the total of 2300
slabs collected.
a. Find E (X-bar) = u = 0.64
----
Var(X-bar) = [0.176/sqrt(400)]^2 = [0.0310]/400 = 0.00007744
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b. Find P(X-bar >.63)
z(0.63) = (0.63-0.64)/[0.176/sqrt(400)] = -1.1364
P(x-bar > 0.63) = P(z > -1.1364) = 0.8721
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Cheers,
Stan H.
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