Hi there!
We are given the equation:
x² - 2y = 7
To verify if each ordered pair is apart of the function, we can plug in their respective x and y values:
1. (5)² - 2(8) = 7
25 - 16 = 9 ≠ 7. This is NOT correct.
2. (-1)² - 2(-3) = 7
1 + 6 = 7. This is correct.
3. (-4)² - 2(-11.5) = 7
16 + 23 = 39 ≠ 7. This is NOT correct.
4. (1.2)² - 2(-2.78) = 7
1.44 +5.56 = 7. This is correct.
Thus, only 1 and 4 are the correct answers.
Answer:
And we can find this probability using the complement rule and with the normal standard table or excel:
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 household spent 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 using the complement rule and with the normal standard table or excel: