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.
what are the options? your question seems incomplete
Answer:
Step-by-step explanation:
J and K are equal
8x - 23 = 6x + 11 Add 23 to both sides
8x = 6x + 11 + 23 Combine the right
8x = 6x + 34 Subtract 6x from both sides
8x - 6x = 34 Combine the left
2x = 34 Divide by 2
x = 34/2
x = 17
=================================
M and L are both supplementary to J and K respectively.
J = 8x - 23
J = 8*17 - 23
J = 136-23
J = 113
K = 113
===================================
M + 113 = 180
M = 180 - 113
M = 67
L = 67
Let
and
be these consecutive integers. For some base
, we can write


If

then

Now,



Squaring both sides gives

and so



(because the base has to be non-zero)