Answer:
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 lifetime for a TV 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 like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Solve for x by simplifying both sides of the equation, then isolating the variable.
x = -22
The benchmarks are: 0, 0.25, 0.50, 0.75 and 1.
2. 81 → 2.75
+
3.73 → 3.75
------------
2.75 + 3.75 = 6.50
Answer:
The answer is B.
Step-by-step explanation:
You have to apply the area of triangle formula :






is a right triangle with base length 1 and height 8, so the area of

is

.
The average value of

over

is given by the ratio

The denominator is just the area of

, which we already know. The average value is then simplified to

In the

-plane, we can describe the region

as all points

that lie between the lines

and

(the lines which coincide with the triangle's base and hypotenuse, respectively), taking

. So, the integral is given by, and evaluates to,


