You found your area wrong as soon as you gt 192 you multiply by 0.50 getting 96 then you divide by 20 to get 4.8 centimeters
Simplify brackets
10x - 4 = 8x + 14
Add 4 to both sides
10x = 8x + 14 + 4
Simplify 8x + 14 + 4 to 8x + 18
10x = 8x + 18
Subtract 8x from both sides
10x - 8x = 18
Simplify 10x - 8x to 2x
2x = 18
Divide both sides by 2
x = 18/2
Simplify 18/2 to 9
<u>x = 9</u>
Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.
P(<em>X</em> ≤ 0.37) = P((<em>X</em> - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(<em>Z</em> ≤ -2)
where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)
Given the required precision for this probability, you should consult a calculator or appropriate <em>z</em>-score table. You would find that
P(<em>Z</em> ≤ -2) ≈ 0.0228
You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,
P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95
which means
P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05
The normal distribution is symmetric, so this means
P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025
which is indeed pretty close to what we found earlier.
