What is the solution of the following systems?
2 answers:
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Answer:
And we can find this probability with the complement rule:
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 average homicide rate for the cities 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 complement rule:
For this case we have the following variables:
x: the number of minutes of television Sam watched each day
y: the number of minutes she spent exercising
Then, we have the following function that models the problem:
if she spends 30 minutes watching television we have x = 30.
Substituting in the given equation we have:
Answer:
the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day is:
72 minutes