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2 answers:
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Given a table of historical demand for a product as follows:
![\begin{tabular} {|c|c|} &Demand\\[1ex] April&60\\ May&55\\ June&75\\July&60\\August&80\\September&75\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0A%20%26Demand%5C%5C%5B1ex%5D%0AApril%2660%5C%5C%0AMay%2655%5C%5C%0AJune%2675%5C%5CJuly%2660%5C%5CAugust%2680%5C%5CSeptember%2675%5C%5C%0A%5Cend%7Btabular%7D)
The linear regression equation is given by
where:
and
We calculate the required values using the following table, where
<span>April = 1, May = 2, and so on.
![\begin{tabular} {|c|c|c|c|} X &Y&X^2&XY\\[1ex] 1&60&1&60\\ 2&55&4&110\\ 3&75&9&225\\ 4&60&16&240\\ 5&80&25&400\\ 6&75&36&450\\[1ex] \Sigma X=21&\Sigma Y=405&\Sigma X^2=91&\Sigma XY=1,485 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%20%0A%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%0AX%20%26Y%26X%5E2%26XY%5C%5C%5B1ex%5D%20%0A1%2660%261%2660%5C%5C%20%0A2%2655%264%26110%5C%5C%20%0A3%2675%269%26225%5C%5C%0A4%2660%2616%26240%5C%5C%0A5%2680%2625%26400%5C%5C%0A6%2675%2636%26450%5C%5C%5B1ex%5D%0A%5CSigma%20X%3D21%26%5CSigma%20Y%3D405%26%5CSigma%20X%5E2%3D91%26%5CSigma%20XY%3D1%2C485%20%0A%5Cend%7Btabular%7D)
Thus,
and
Therefore, the </span><span>trend line for the historical data is given by
</span>
The linear regression equation is given by
where:
and
We calculate the required values using the following table, where
<span>April = 1, May = 2, and so on.
Thus,
and
Therefore, the </span><span>trend line for the historical data is given by
Answer:
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
54% of the school's graduates move to a different state after graduating.
This means that
7 randomly selected graduates
This means that
Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Either none moves, or at least one does. The sum of the probabilities of these events is 1. So
We want . Then
In which
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.