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:
I think the answer is 2 dollars
Step-by-step explanation:
Polygons include
triangles
rectangle
square
pentagon
hexagon
etc.
The answer is probably the opposite which in this case would be -19 ?
Answer: The number is 10.
Step-by-step explanation:
Let x be the required number.
Given: 11 is multiplied to the number then 24 is subtracted from that and the result is 86.
The mathematical statement for the given situation,
11x -24 = 86
To solve the equation, Add 24 on both sides , we get
11x - 24 +24 = 86+24
⇒ 11x = 110
Divide both sides by 11, we get
x = 10
hence, the number is 10.
