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.
Answer:
A. Sin 2x
Step-by-step explanation:
This is a trig function and has the shape of sine or cosine. Since it intersects at (0,0), it is likely a sine graph. A normal sine graph starts at (0,0), crests up at 1, and crosses back down at the x-axis at (3.14, 0). However, this graph starts at (0,0) and crosses back again at half that value. This graph has been horizontally compressed by multiplication of a number greater than 1. So this graph is Sin 2x.
Answer:
x=√−16n−28 or x=−√−16n−28
Step-by-step explanation:
Step 1: Add -16n to both sides.
x2+16n+28+−16n=0+−16n
x2+28=−16n
Step 2: Add -28 to both sides.
x2+28+−28=−16n+−28
x2=−16n−28
Step 3: Take square root.
x=√−16n−28 or x=−√−16n−28
34=2x + 16
18=2x
x=9
Robert used 9 grams of iron filings in his first experiment.
Step-by-step explanation:
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