Math / Data & Statistics

QuestionThe number of square feet per house have an unknown distribution with mean 1670 and standard deviation 140 square feet. A sample, with size $n=48$ , is randomly drawn from the population and the values are added together. Using the Central Limit Theorem for Sums, what is the mean for the sample sum distribution?
Provide your answer below: $\square$ square feet

Studdy Solution

STEP 1

1. The population mean is $\mu = 1670$ square feet.
2. The population standard deviation is $\sigma = 140$ square feet.
3. The sample size is $n = 48$ .
4. We are using the Central Limit Theorem for Sums.

STEP 2

1. Understand the Central Limit Theorem for Sums.
2. Calculate the mean of the sample sum distribution.

STEP 3

The Central Limit Theorem for Sums states that the distribution of the sum of a large number of independent, identically distributed variables will be approximately normal, regardless of the shape of the original distribution. The mean of the sample sum distribution is given by:
$\mu_{\text{sum}} = n \times \mu$

STEP 4

Substitute the given values into the formula for the mean of the sample sum distribution:
$\mu_{\text{sum}} = 48 \times 1670$
Calculate the result:
$\mu_{\text{sum}} = 80160$
The mean for the sample sum distribution is:
$\boxed{80160}$ square feet

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