Calculate the area of the shaded region
1 answer:
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Answer:
And we can find this probability with the following difference:
And in order to find these probabilities we can find 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 variable of interest 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 find tables for the normal standard distribution, excel or a calculator.
It is given in the question that
And we have to find the value of
Substituting the values of two functions, we will get
8x^3 is common in the numerator, and on taking it out, we will get
And that's the required answer .