At a certain grocery store 65% of the customers regularly use coupons.
what is the approximate standard deviation of the sampling distribution of the proportion for
samples of size 340?
a.11.1%
b.6.7%
c.4.4%
d.2.6%

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Ответ:

Kelbee781

19.07.2020

Mathematics

$\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{ k }}x
\end{array}\\\\
-----------------------------\\\\$

$\bf \textit{"y" varies directly as the square root of "x"}\implies \boxed{y=k\sqrt{x}}
\\\\\\
\textit{now, we also know that }
\begin{cases}
y=29\\
x=100
\end{cases}\implies 29=k\sqrt{100}\implies 29=10k
\\\\\\
\cfrac{29}{10}=k\textit{ so, the equation is then }\implies y=\cfrac{29}{10}\sqrt{x}
\\\\\\
\textit{what's "y" when x=123?}\qquad well\quad y=\cfrac{29}{10}\sqrt{123}\implies y\approx 32.16256$

bear in mind that, constant variation, either direct or inverse type, involves a "k" or a constant of variation value

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At a certain grocery store 65% of the customers regularly use coupons. what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 340? a.11.1% b.6.7% c.4.4% d.2.6%