,
, By the Central Limit Theorem, the means of the two distributions are the same:
μx¯=μ=2,500,000
To find the Standard Deviation of the sampling distribution, we divide the population
standard deviation by the square root of the sample size:
σx¯=σn−−√=625,00050−−√≈88,388
3. Question
A bank is reviewing its risk management policies with regards to mortgages. To
minimize the risk of lending, the bank wants to compare the typical mortgage owed by
their clients against other homebuyers. The average mortgage owed by Americans is
$306,500, with a standard deviation of $24,500. Suppose a random sample of
150Americans is selected.
Identify each of the following, rounding your answers to the nearest cent when
appropriate:
We are given population mean μ=$306,500and population standard deviation
σ=$24,500, and want to find the mean and standard error of the sampling
distribution, μx¯and σx¯for samples of size n=150.
By the Central Limit Theorem, the means of the two distributions are the same:
μx¯=μ=$306,500
To find the Standard Deviation of the sampling distribution, we divide the population
standard deviation by the square root of the sample size:
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