Explain how collecting mean values (X-bar) from samples drawn from a dataset, regardless of the statistical distribution of the
1 answer:
Answer:
The response is presented below
Explanation:
Central Limit Theorem: The CLT is a statistical principle asserting that if a sample size is sufficiently large and shows minimal variation from the population, the average of all samples will approximate the mean of that population. Furthermore, all distributions can be modeled as nearly normal.
This principle is illustrated by the central limit theorem. Specifically, if we gather independent random samples of size n from any kind of population, a large n will yield a sample distribution that aligns with a normal distribution pattern.
mean of the sample means
.............1
while the standard deviation of the sample means is
.........2
and This theory has findings applicable elsewhere in statistical studies. Although it may initially seem theoretical and lacking real-world utility, the Central Limit Theorem is crucial for applying statistics effectively in practice.
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Answer:
total expense for the new boiler = $229706.825
total expense for new boiler = $127512
Explanation:
provided information
initial power p1 = 80 kW
price C = $160000
cost index CI 1 = 187
cost index CI 2= 194
capacity factor f = 0.6
subsequent power p2 = 120 kW
present cost = $18000
to determine
total expense and cost for 40 kW
solution
we evaluate CN cost for the new boiler and CO cost for the existing boiler
where x represents the capacity of the new boiler
first we compute the current cost of the old boiler which is
current cost CO = C × .............1
substituting the value here
current cost = 160000 ×
updated current cost = $165989.304
and
employing power sizing strategy for 124 kW
CN/CO = ...............2
insert value and calculate CN
CN/CO =
CN / 165989.304 =
CN = 211706.825
therefore the new expense = $211706.825
hence
total expense for the new boiler amounts to
total expense = new expense + current cost
total exp = 211706.825 + 18000
boiler expense total = $229706.825
and
concerning a 40 kW unit, the calculated new cost will be
applying equation 2
CN/CO =
CN / 165989.304 =
CN = 109512
thus the new cost is $109512
therefore
total expense for the new boiler is
total exp = new cost + current cost
total expense = 109512 + 18000
total cost for the new boiler = $127512