Trisaba
  • Trisaba
P(x> or = x line over + 2 standard deviation) medal and fan
Mathematics
chestercat
  • chestercat
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Trisaba
  • Trisaba
i got one more two similar
Trisaba
  • Trisaba
normal distributions
Trisaba
  • Trisaba
x line over means there is a line over the x

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Trisaba
  • Trisaba
Trisaba
  • Trisaba
Trisaba
  • Trisaba
someone
anonymous
  • 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
Trisaba
  • Trisaba
it has no labels they want like 68% is 34% + 34%
Trisaba
  • Trisaba
Trisaba
  • Trisaba
we have to use the normal ditribution example ones from this line to this
Trisaba
  • Trisaba
Trisaba
  • Trisaba
3 and 4
Trisaba
  • Trisaba
4 and 5 sorry wrong numbers
Trisaba
  • Trisaba
what am i supposed to do
anonymous
  • 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 \[\begin{cases} D=E=34\\ C=F=13.5\\ B=G=2.35\\ A=H=0.15 \end{cases}\]
Trisaba
  • Trisaba
where is x
anonymous
  • anonymous
So for your first problem, \[P(x\ge \bar{x}+2\sigma)=G+H=\cdots\]
Trisaba
  • Trisaba
x with the line over it is the mean
anonymous
  • anonymous
I have \(\bar{x}\) labeled on the graph above in the middle of the curve.
Trisaba
  • Trisaba
i know
Trisaba
  • Trisaba
im confused
anonymous
  • 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.
Trisaba
  • Trisaba
how did you do that
anonymous
  • 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 \(H=0.15\)?
Trisaba
  • Trisaba
i thought h is 1.15
Trisaba
  • Trisaba
nevermind
anonymous
  • 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 \[\begin{align*}1&=A+B+C+D+E+F+G+H\\ 1&=A+99.7+H\\ 0.3&=A+H\\ 0.3&=A+A\\ 0.3&=2A\\ 0.15&=A=H \end{align*}\]
Trisaba
  • Trisaba
what is x though
anonymous
  • 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?
Trisaba
  • Trisaba
yes
Trisaba
  • Trisaba
so the answer is a group of probabilities?
anonymous
  • 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 \(A+B+C+D+E\).
Trisaba
  • Trisaba
and 4?
anonymous
  • anonymous
\[P(x\ge \bar{x}+2\sigma)=G+H\]
Trisaba
  • Trisaba
2.5?
anonymous
  • anonymous
Yes
Trisaba
  • Trisaba
thank you so much
anonymous
  • anonymous
yw
Trisaba
  • Trisaba
bye
Trisaba
  • Trisaba
wait actually i forgot 6 too
Trisaba
  • Trisaba
Trisaba
  • Trisaba
nevermind

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