SOLUTION: The property tax paid by homeowners in a large city was determined to be normally distributed with a mean of $2,800 and a standard deviation of $400. A random sample of four homes

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Question 1163064: The property tax paid by homeowners in a large city was determined to be normally distributed with a mean of $2,800 and a standard deviation of $400. A random sample of four homes was drawn.
a. What is the probability distribution of the mean of the sample of four homes?
b. Determine the probability that the sample mean falls between $2,500 and $2,900
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
It is normal with mean $2800 and sd $400/sqrt(4) or $200. ~N(2800, 200)
The z-value for part b is (x bar-mean)/sigma/sqrt(n)
this is 100/200 or 0.5
and -300/200 or -1.5
that probability is 0.6247,