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:
8 units
Step-by-step explanation:
it should be 8, EH is practically AD, if you match ABCD's letters and numbers with EFGH's. I hope this helps!
Answer:6
Step-by-step explanation:Reorder
2
2
and
−
x
-
x
.
y
=
−
x
+
2
y
=
-
x
+
2
3
x
+
3
y
=
6
3
x
+
3
y
=
6
Replace all occurrences of
y
y
in
3
x
+
3
y
=
6
3
x
+
3
y
=
6
with
−
x
+
2
-
x
+
2
.
y
=
−
x
+
2
y
=
-
x
+
2
3
x
+
3
(
−
x
+
2
)
=
6
3
x
+
3
(
-
x
+
2
)
=
6
Simplify
3
x
+
3
(
−
x
+
2
)
3
x
+
3
(
-
x
+
2
)
.
Tap for more steps...
y
=
−
x
+
2
y
=
-
x
+
2
6
=
6
6
=
6
Since
6
=
6
6
=
6
, the equation will always be true.
y
=
−
x
+
2
y
=
-
x
+
2
Always true
Remove any equations from the system that are always true.
y
=
−
x
+
2
Answer:
Step-by-step explanation:
We are given that
Differentiate w.r.t x
By using formula
Hence, the derivative of function
