ExitUse the clustering estimation technique to find the approximate total in the following question.What is the estimated sum of
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Answer:
And for the other case if we use the z score and the complement rule we have:
And we can find the probability of interest like this:
And replacing we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
We assume that the distribution is
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we find the individual probabilities we got:
And for the other case if we use the z score and the complement rule we have:
And we can find the probability of interest like this:
And replacing we got: