Answer:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of gallons of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Hi there!
To start, we can use the two points to find the slope using the formula y2-y1/x2-x1. Just sub in the points and solve!
-0.5-0.5/3-(-3)
-1/6
Sub that into the formula y-mx+b for m, and use one of the points for x and y - solve for b and you get your equation.
y=mx+b
y=-1/6x+b
0.5=-1/6*-3+b
0.5=-0.5+b
0.5+0.5=b
b=1
Therefore your equation is y=-1/6x+1
Hope this helps!
Answer:
FIRST EXPRESSION:
- If
, the value of
is 
- If
, the value of
is 
- If
, the value of
is 
SECOND EXPRESSION:
- If
, the value of
is 
- If
, the value of
is 
- If
, the value of
is 
Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.
Step-by-step explanation:
Substitute the given values of "b" into each expression and evaluate.
- For the first expression
, you get:
If
→ 
If
→ 
If
→ 
- For the second expression
, you get:
If
→ 
If
→ 
If
→ 
You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.
B, 1.2, is greater in value than 115%