e select a random sample of size forty recently issued building permits for improvements to existing residential structures and record the value, X, of each permit. Prior experience has shown that, in Worcester County, the relative frequency distribution for the value of such building permits has a mean of $8,000 and a standard deviation of $1,
Suppose we select a random sample of size forty recently issued building permits for improvements to existing residential structures and record the value, X, of each permit. Prior experience has shown that, in Worcester County, the relative frequency distribution for the value of such building permits has a mean of $8,000 and a standard deviation of $1,500.
a). Describe carefully the sampling distribution of the
b). What is the
c). What is the probability that the mean value of the permits in the sample will be between $7,500 and $8,500?
(a)
As the population standard deviation is known, it can be said that the distribution follows the normal distribution. The mean and standard deviation of the sampling distribution of the sample mean is equal to μXˉ and respectively.
For this case, the mean will be 8,000 and the standard deviation will be
Hence, the sampling distribution of the mean value of a sample of forty building permits is written as:
X∼N(8000, 237.171 )
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