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 April 20th, 2018, 07:45 PM #1 Member   Joined: Mar 2017 From: Israel Posts: 85 Thanks: 2 Statistics Hello Can you help me please about the next exercise: The weight of a third-generation mobile phone is normal (normal distribution), with an average of 96 grams. It is known that 90% of these phones are between 88 grams and 104 grams. The first question was to find standard deviation of the phones weight, I found it (if I didn't made a mistake): So the standard deviation is 4.863 (from table Z). Now there is another question: What is the weight that only 2.5% of these phones weigh less? I tried to find but i had insane answers So... I don't know how to find it (maybe i miss something). Thanks!
 April 20th, 2018, 08:01 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,582 Thanks: 1427 $\Phi^{-1}(0.025) = -1.960$ $\sigma = 4.86365$ $\dfrac{w - 96}{ 4.86365} = -1.960$ $w = 86.467~g$ Thanks from IlanSherer
April 20th, 2018, 10:53 PM   #3
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Quote:
 Originally Posted by romsek $\Phi^{-1}(0.025) = -1.960$ $\sigma = 4.86365$ $\dfrac{w - 96}{ 4.86365} = -1.960$ $w = 86.467~g$

I just didn't understand why exponentiation of minus 1.

April 20th, 2018, 11:17 PM   #4
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Quote:
 Originally Posted by IlanSherer Thanks for answering I just didn't understand why exponentiation of minus 1.
that's the inverse CDF of the normal distribution.

It's the same old table lookup you're used to doing.

April 21st, 2018, 12:20 AM   #5
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Quote:
 Originally Posted by romsek that's the inverse CDF of the normal distribution. It's the same old table lookup you're used to doing.
If the question was "What is the weight that only 2.5% of these phones weigh above?", then the exponentiation is 1, right?

April 21st, 2018, 05:59 AM   #6
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Quote:
 Originally Posted by romsek that's the inverse CDF of the normal distribution. It's the same old table lookup you're used to doing.
Oh I'm sorry about last quote, I was tired and i wasn't in focus.
Now I understood, thanks for help!

Have a good week

April 21st, 2018, 09:17 AM   #7
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Quote:
 Originally Posted by IlanSherer If the question was "What is the weight that only 2.5% of these phones weigh above?", then the exponentiation is 1, right?
it's not exponentiation.

it's the symbology for an inverse function

April 27th, 2018, 04:30 PM   #8
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Quote:
 Originally Posted by romsek it's not exponentiation. it's the symbology for an inverse function
Thanks
There is another question in same exercise (which I wrote in the current post), can you tell me please if I solved correctly?

The question is:
What is the relative frequency of 3G (third-generation) phones weighing more than 100 grams?

Because of normal distribution and there is 90% in 88-104 grams, then in 100-104 grams there is 22.5%, and above 104 there is 5%, therefore the answer is 22.5%+5%=27.5%=0.275

Right?

April 27th, 2018, 05:15 PM   #9
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Quote:
 Originally Posted by IlanSherer Thanks There is another question in same exercise (which I wrote in the current post), can you tell me please if I solved correctly? The question is: What is the relative frequency of 3G (third-generation) phones weighing more than 100 grams? My answer: Because of normal distribution and there is 90% in 88-104 grams, then in 100-104 grams there is 22.5%, and above 104 there is 5%, therefore the answer is 22.5%+5%=27.5%=0.275 Right?
$1-\Phi\left(\dfrac{100-96}{4.86365}\right)=0.205417$

April 28th, 2018, 02:13 AM   #10
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Quote:
 Originally Posted by romsek $1-\Phi\left(\dfrac{100-96}{4.86365}\right)=0.205417$
Thanks again
If the question was about less than 100 grams, then the answer was only:

Φ((100−96)/4.86365)

Right?

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