Statistics help :(

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Martin84a

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Jan 1, 2009
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Thanks a lot guys you have no idea how much I appreciated it! :D I have a few more assignments that I could use some help with if anyone knows the answer :)

4-17) Find z such that P(Z>z) = 0.12
The answer is 1.175

I don't know how to start with this one. First of all, if Z is the standard normal distribution, then what is z? I'm not really sure what they mean when they write Z>z or X>x. Else what should I do?

The Z value 0.12 gives a probability of 0.0478
If I need to find the Z value where the probability is 0.12, then it's between 0.30 (0.1179) and 0.31 (0.1217)



4-39 For a normal random variable with mean 16.5 and standard deviation 0.8, find a point of the distribution such that there is a 0.85 probability that the value of the random variable will be above it.

What should I do here?


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Solved!

4-21. The deviation of a magnetic needle from the magnetic pole in a certain area in northern Canada is a normally distributed random variable with the mean 0 and standard deviation 1. What is the probability that the absolute value of the deviation from the north pole at a given moment will be more than 2.4?

Ok, since mean is 0 and std. dev. is 1, it's a Z distribution. So they are asking "what is the chance of Z>2.4" right? I can then look in my table and find P(Z>2.4) = 0.4918. But since the table measures from 0 to infinity, we have to add 0.5 to our number. So 0.5+0.4918=0.9918. So the area from minus infinity to 2.4 is 99.18%, but we are asked to find the chance of it being larger than 2.4. So we take the inverse of it and find 1-99.18 = 0.0082%. Right now I would say I'm done but the result is supposed to be 0.0162%. I can see that if I multiply my result then I'll get that number, but I don't see why I have to do so :( Have I done something wrong?


4-33 - Fluctations on a French CAC-40 stock index from march to june 1997 seem to follow a normal distribution with mean 2600 and standard deviation of 50. Find the probability that the CAC-40 stock
will be between 2520 and 2670 on a random day in the period of study.

Here I'll transform X to Z using P(a < X < b) = P (a -&#956; / &#963; < Z < b - &#956; / &#963;)

So 2520-2600/50 = -0.8
and 2670-2600/50 = 1.4

Meaning P(-0.8 < Z < 1.4)

Now this should be easy here on, but I can't get the right result.
I look in my table and find 0.8 = 0.2881 and 1.4 = 0.4192. So by adding the numbers I should get the area between -0.8 and 1.4, right? I get 0.7073 but I should get 0.8644 :(
 
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busydude

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Feb 5, 2010
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For the first one..you need to multiply your answer with 2 because they asked you to find the probability of the absolute deviation.
 

Gibson486

Lifer
Aug 9, 2000
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F that....I remember when I finished engineering statistics. It was the happiest day of my life.
 

Martin84a

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Thank you very much for seeing the error in the second one! :D I still don't quite get the first answer though. Perhaps I've missed something in my book, but what is the absolute probability compared to just saying the probability?
 

TecHNooB

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Sep 10, 2005
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Thank you very much for seeing the error in the second one! :D I still don't quite get the first answer though. Perhaps I've missed something in my book, but what is the absolute probability compared to just saying the probability?

It's the probability of the absolute deviation, not absolute probability.
 

busydude

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Feb 5, 2010
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Absolute deviation of greater than 2.4 means that the +ve deviation is greater than 2.4 and the -ve deviation is less than -2.4.

And since normal distribution is symmetric.. Both sides will have equal area. So the final answer is 2 times of what you got.. Since you only calculated the + ve deviation.
 
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Martin84a

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Hm..I still don't get it :/ I mean, while Z is symmetrical we still measure from minus infinity and towards plus infinity when we need to find the probability of an area, right?. So why do we all of sudden measure in both sides of the distribution? :eek:
 
Feb 25, 2011
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Hm..I still don't get it :/ I mean, while Z is symmetrical we still measure from minus infinity and towards plus infinity when we need to find the probability of an area, right?. So why do we all of sudden measure in both sides of the distribution? :eek:

Because compass needles can move either right or left.

/liberal arts major
 

Martin84a

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Jan 1, 2009
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So when it's about the absolute deviation, I always have to find both +Z and -Z, and it will always be symmetrical?
 

Fayd

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Jun 28, 2001
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www.manwhoring.com
Hi, I have been stuck with my statistics assignments for ages now so I hope you guys can help me out.

4-21. The deviation of a magnetic needle from the magnetic pole in a certain area in northern Canada is a normally distributed random variable with the mean 0 and standard deviation 1. What is the probability that the absolute value of the deviation from the north pole at a given moment will be more than 2.4?

Ok, since mean is 0 and std. dev. is 1, it's a Z distribution. So they are asking "what is the chance of Z>2.4" right? I can then look in my table and find P(Z>2.4) = 0.4918. But since the table measures from 0 to infinity, we have to add 0.5 to our number. So 0.5+0.4918=0.9918. So the area from minus infinity to 2.4 is 99.18%, but we are asked to find the chance of it being larger than 2.4. So we take the inverse of it and find 1-99.18 = 0.0082%. Right now I would say I'm done but the result is supposed to be 0.0162%. I can see that if I multiply my result then I'll get that number, but I don't see why I have to do so :( Have I done something wrong?


abs value of deviation means going in both directions.

ie, the chance of it being < -2.4, and >2.4

so you need to add value of -infinity to -2.4, + 2.4 to infinity. which works out to be .0162%.
 

Martin84a

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Jan 1, 2009
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Thanks to all of you :) I have added the assignments where I'm currently stuck to the main post :p
 
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