Stat help

[Q]

I had Statistics in high school so I'm pretty decent on this stuff but for some reason I cannot get this problem right. This is for studying, not a HW problem.



Suppose X ~ N(10, 4)
If P(x0 < X < 14) = 0.7783, find x0.

I keep getting 16.12, while the answer is apparently 3.88

If there are any math whizzes that could help me out, I'd appreciate it.

 

[Juked07]

Normalize and looket the chart?

 

[DrPizza]

It's been a very long time for me, so I'm unsure of the notation. Does the N(10,4) mean that x is normally distributed with a mean of 10 and a standard deviation of 4?

For what it's worth, how did you get 16.12? I'm assuming the latter half of the question is "the probability that X is greater than x0 and less than 14 (between x0 and 14) is .7783

And, from the looks of your answer, I have a sneaky suspicion that you added when you should have subtracted (or vice versa)

 

[speg]

If you're looking for X between x0 and 14 - then you know your answer of 16 is way off....

I'll get back to you on the rest

Yeah, here you go:

10 - 1.53 * 4 = 3.88
--------------------------

So you know the mean is 10. SD is 4.

You want to know x0 if the probability of X between x0 and 14 is 0.7783

Well, 14 is 1 SD from the mean. So look up the probability it is between 10 and 14 on the Z-Table for Z=1 and you get 0.3413

But you want the total probability to be 0.7783 so you still need 0.7783-0.3413 = 0.437 on the low end.

So, look up the Z-Score for 0.437 -> Z=1.53 Now you know where your low end should be: 10 - 1.53 * 4 = 3.88

(10 + 1.53 * 4 = 16.12 was your mistake)

 

[Q]

Ahh I see speg, the x0 was to the left of the mean so that makes it a negative Z value, so my 6.12 should have been -6.12

Thanks!

 

[Net]

you should go on irc.

irc.linux.org #math

www.mirc.com

real-time help. and their extremely good.

 

[blinky8225]

Hmm, I always thought the second parameter is the variance, not standard deviation? Perhaps some textbooks do it differently