## Trisaba one year ago P(x> or = x line over + 2 standard deviation) medal and fan

1. Trisaba

i got one more two similar

2. Trisaba

normal distributions

3. Trisaba

x line over means there is a line over the x

4. Trisaba

@superman36

5. Trisaba

@Jaynator495

6. Trisaba

someone

7. anonymous

$P(x\ge \bar{x}+2\sigma)~~?$ How is $$x$$ distributed? If you're given a normal distribution, this is straightforward if you know the empirical rule: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

8. Trisaba

it has no labels they want like 68% is 34% + 34%

9. Trisaba

@SithsAndGiggles

10. Trisaba

we have to use the normal ditribution example ones from this line to this

11. Trisaba

12. Trisaba

3 and 4

13. Trisaba

4 and 5 sorry wrong numbers

14. Trisaba

what am i supposed to do

15. anonymous

|dw:1441842345311:dw| From the rule, you have that $\begin{cases} D+E=68\\ C+D+E+F=95\\ B+C+D+E+F+G=99.7\\ A+B+C+D+E+F+G+H=1 \end{cases}$ The distribution is symmetric, so you can determine that $\begin{cases} D=E=34\\ C=F=13.5\\ B=G=2.35\\ A=H=0.15 \end{cases}$

16. Trisaba

where is x

17. anonymous

So for your first problem, $P(x\ge \bar{x}+2\sigma)=G+H=\cdots$

18. Trisaba

x with the line over it is the mean

19. anonymous

I have $$\bar{x}$$ labeled on the graph above in the middle of the curve.

20. Trisaba

i know

21. Trisaba

im confused

22. anonymous

All I've done is rephrase the problem from $$P(x\ge\bar{x}+2\sigma)$$ to the simple operation $$2.35+0.15$$. The areas of the regions are probabilities.

23. Trisaba

how did you do that

24. anonymous

The area of the shaded region is the probability you're looking for: |dw:1441843152498:dw| Are you wondering how I found $$G=2.35$$ and $$H=0.15$$?

25. Trisaba

i thought h is 1.15

26. Trisaba

nevermind

27. anonymous

Well, we have $B+C+D+E+F+G=99.7$ so substituting this into the total probability equation (the last equation in the system above), we get \begin{align*}1&=A+B+C+D+E+F+G+H\\ 1&=A+99.7+H\\ 0.3&=A+H\\ 0.3&=A+A\\ 0.3&=2A\\ 0.15&=A=H \end{align*}

28. Trisaba

what is x though

29. anonymous

$$x$$ is completely symbolic here. It's referring to some event or characteristic that occurs with probability modeled by the curve. It can take on any value in the domain of the distribution. Let's say we're talking about the heights of a large group of people. $$\bar{x}$$ is the average of height, while $$x$$ can be any height that is seen among the group of people. So as an example, the statement $$P(x=5)$$ is the same as "the probability that any given person's height is $$5$$ (units)". Meanwhile, $$P(x>5)$$ means "the probability that any given person's height is greater than $$5$$", and so on. Does that make sense?

30. Trisaba

yes

31. Trisaba

so the answer is a group of probabilities?

32. anonymous

The answers are the sums of the areas that belong in the desired intervals. I've already shaded the one you're interested in for (4). (5) is just as easy: |dw:1441844287564:dw| or $$A+B+C+D+E$$.

33. Trisaba

and 4?

34. anonymous

$P(x\ge \bar{x}+2\sigma)=G+H$

35. Trisaba

2.5?

36. anonymous

Yes

37. Trisaba

thank you so much

38. anonymous

yw

39. Trisaba

bye

40. Trisaba

wait actually i forgot 6 too

41. Trisaba