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3 years ago

An art gallery sells paintings at .35 per square inch

Mathematics

1 answer:

VashaNatasha [74]3 years ago

6 0

1 foot = 12 inches

2 x 12 = 24 +3 = 27 inches

3 x 12 = 36 +5 = 41 inches

27*41 = 1107 square inches

1107 * 0.35 = $387.45

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

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

So,

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So,

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

Since $z_1$ and $z_2$ 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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4 years ago