How do you graph a linear inequality?
1 answer:
Step-by-step explanation:
Change the sign of inequality to sign of equation.
First step:
Calculate the coordinates of two points of a line.
Choice any two values of x, put it to the equation and calculate the values of y.
Example:
y > 2x + 1 → y = 2x + 1
for x = 0 → y = 2(0) + 1 = 0 + 1 = 1 → (0, 1)
for x = -1 → y = 2(-1) + 1 = -2 + 1 = -1 → (-1, -1)
Draw a line passing through the given points.
If is < or >, then draw dot line.
If is ≤ or ≥, then draw solid line.
In our example, we have an inequality sign: >. Therefore, draw a dot line.
Second step:
Shading region:
If is < or ≤ - shading to the left.
If is > or ≥ - shading to the right.
In our example, we have an inequality sign: >. Therefore, shading to the right.
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Answer:
a) Figure attached
b)
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 this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
c)
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
d)
And using the z score we got:
And that correspond to approximately 0.15%
Step-by-step explanation:
Part a
For this case we can see the figure attached.
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".
Part b
Let X the random variable that represent the length of human pregnancy of a population, and for this case we know that:
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 this difference:
An we know using the graph in part a that this area correspond to 0.95 or 95%
Part c
And we can find this probability with this difference:
An we know using the graph in part a that this area correspond to 0.95 or 34+34+13.5+2.35%=83.85%
Part d
We want this probability:
And using the z score we got:
And that correspond to approximately 0.15%
