Let's say you want to compute the probability

where

converges in distribution to

, and

follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing

such that its mean and variance are the same as those for

.
Example: If

is binomially distributed with

and

, then

has mean

and variance

. So you can approximate a probability in terms of

with a probability in terms of

:

where

follows the standard normal distribution.
Answer:
d
Step-by-step explanation:
Given y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of proportion
To find k use the condition y =
when x =
, then
= k(
)² =
k ( multiply both sides by 8 )
1 = 2k ( divide both sides by 2 )
k = 
y =
x² ← equation of proportion
When y =
, then
=
x² ( multiply both sides by 2 )
9 = x² ( take the square root of both sides )
x = ±
= ± 3
with positive value x = 3 → d
Answer:
1. 8.85 quarts
2. 44.25%
Step-by-step explanation:
In 15 quarts of a solution with percentage of antifreeze = 35%
Amount of antifreeze = 35% × 15
= 0.35 × 15
= 5.25 quarts
that solution is mixed with 5 quarts of a solution with percentage of antifreeze = 72%
Amount of antifreeze = 72% × 5
= 0.72 × 5
= 3.6 quarts
Total amount of mixture = 15 quarts + 5 quarts = 20 quarts
1. Now we will calculate the total amount of antifreeze in the resulting mixture.
= 5.25 + 3.6 = 8.85 quarts
2. The percentage of the resulting mixture is antifreeze
= 
= 44.25%
1. total amount of antifreeze is 8.85 quarts
2. the percentage of antifreeze is 44.25%
Solutions
First Lets solve for this equation
Therefore this given equation is a <span>dependent system.
</span>
<span>Solve for </span>
There are too many solutions to these equations.