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 IlanSherer April 20th, 2018 07:45 PM

Statistics

Hello :)

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):

https://i.imgur.com/HbBEfnH.png

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?

So... I don't know how to find it (maybe i miss something).

Thanks!

 romsek April 20th, 2018 08:01 PM

$\Phi^{-1}(0.025) = -1.960$

$\sigma = 4.86365$

$\dfrac{w - 96}{ 4.86365} = -1.960$

$w = 86.467~g$

 IlanSherer April 20th, 2018 10:53 PM

Quote:
 Originally Posted by romsek (Post 593047) $\Phi^{-1}(0.025) = -1.960$ $\sigma = 4.86365$ $\dfrac{w - 96}{ 4.86365} = -1.960$ $w = 86.467~g$

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

 romsek April 20th, 2018 11:17 PM

Quote:
 Originally Posted by IlanSherer (Post 593053) 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.

 IlanSherer April 21st, 2018 12:20 AM

Quote:
 Originally Posted by romsek (Post 593057) 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?

 IlanSherer April 21st, 2018 05:59 AM

Quote:
 Originally Posted by romsek (Post 593057) 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 :)

 romsek April 21st, 2018 09:17 AM

Quote:
 Originally Posted by IlanSherer (Post 593063) 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

 IlanSherer April 27th, 2018 04:30 PM

Quote:
 Originally Posted by romsek (Post 593077) 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?

 romsek April 27th, 2018 05:15 PM

Quote:
 Originally Posted by IlanSherer (Post 593398) 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?
$1-\Phi\left(\dfrac{100-96}{4.86365}\right)=0.205417$

 IlanSherer April 28th, 2018 02:13 AM

Quote:
 Originally Posted by romsek (Post 593402) $1-\Phi\left(\dfrac{100-96}{4.86365}\right)=0.205417$
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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