A rectangular prism has a length on 20in a width of 2 in and a height of 3 1/4in. the prism is filled with cubes that have an edge length of 1/4 how many cubes are needed to fill the rectangular prism? PLEASE HELP THIS IS DUE VERY VERY SOON

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Ответ:

ewilly01

04.03.2020

Mathematics

0.533

Explanation: Note that

$x \ \textgreater \ I \\ \Leftrightarrow x - 0.3 \ \textgreater \ I - 0.3 \\ \\ \Leftrightarrow \boxed{\frac{x - 0.3}{0.1} \ \textgreater \ \frac{I - 0.3}{0.1}} (1)$

Let

z_1

= z-score for I.
z_2

= z-score for x.

The formula for z-score is given by

$\text{z-score} = \frac{(\text{data point}) - (\text{mean})}{(\text{standard deviation})}$

So,

$z_2 = \frac{x - 0.3}{0.1}$

$z_1 = \frac{I - 0.3}{0.1}$

Based on inequality in (1),

$z_2 \ z_1$

So,

$P(x \ \textgreater \ I) = 0.01
\\
\\ \Leftrightarrow P \left (\frac{x - 0.3}{0.1} \ \textgreater \ \frac{I - 0.3}{0.1} \right ) = 0.01 
\\
\\ \Leftrightarrow P(z_2 \ \textgreater \ z_1) = 0.01
\\
\\ \Leftrightarrow 1 - P(z_2 \leq z_1) = 0.01
\\
\\ \Leftrightarrow \boxed{P(z_2 \leq z_1) = 0.99}$

Since z_1

and

are z-scores and the level of nitrogen oxides are normally distributed, using normal distribution calculator (or table),

$z_1 = 2.326
\\
\\ \Leftrightarrow \frac{I - 0.3}{0.1} = 2.326
\\
\\ \Leftrightarrow I - 0.3 = 0.1(2.326)
\\
\\ \Leftrightarrow I - 0.03 = 0.2326
\\
\\ \Leftrightarrow \boxed{I \approx 0.533}$

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