SOLUTION: Hi I really do need your help on this one. Thanks Rivers Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of

Question 162405: Hi I really do need your help on this one. Thanks Rivers
Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?
a. 0.3174
b. 0.1587
c. 0, because it is assumed that the sample mean is equal to the population mean in a normally distributed population.
d.Cannot be determined from the information given.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?
-------------------------
Mean of the sample means = u
Standard deviation of the sample means = 20000/sqrt(16) = 5000
-------------------------
You want the probability of the mean of a sample of size 16 being
less than 15000 or greater than 25000.
That probability is the same as the probability that "z" is less than
-1 or greater than 1. That probability is 0.3173105....
=============================
Cheers,
Stan H.

a. 0.3174
b. 0.1587
c. 0, because it is assumed that the sample mean is equal to the population mean in a normally distributed population.
d.Cannot be determined from the information given.

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