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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: JV-12 on October 14, 2012, 08:27:47 pm

Title: Normal distribution help!
Post by: JV-12 on October 14, 2012, 08:27:47 pm: The weight of cats is normally distributed. It is known that 10% of cats weigh more than 1.8 kg and 15% of cats weigh less than 1.35 kg. Find the mean and the standard deviation of this distribution.

anyone have any ideas how to solve this question?
thanks!
Title: Re: Normal distribution help!
Post by: Jenny_2108 on October 14, 2012, 08:31:20 pm: Quote from: JV-12 on October 14, 2012, 08:27:47 pm
The weight of cats is normally distributed. It is known that 10% of cats weigh more than 1.8 kg and 15% of cats weigh less than 1.35 kg. Find the mean and the standard deviation of this distribution.

anyone have any ideas how to solve this question?
thanks!

Pr(X<1.35)=0.15
Pr(X<1.8 )=0.9

Solve these equations:

$\frac{1.35-\mu}{\sigma}=invNorm(0.15)$

$\frac{1.8-\mu}{\sigma}=invNorm(0.9)$

Edit: type wrong
Title: Re: Normal distribution help!
Post by: JV-12 on October 14, 2012, 08:41:22 pm: would i solve the equations simultaneously?
Title: Re: Normal distribution help!
Post by: HERculina on October 14, 2012, 08:42:31 pm: Yep you would.
Title: Re: Normal distribution help!
Post by: JV-12 on October 14, 2012, 08:49:57 pm: i'm still confused...my calculator came up with "no solutions"
Title: Re: Normal distribution help!
Post by: Jenny_2108 on October 14, 2012, 08:54:20 pm: Quote from: JV-12 on October 14, 2012, 08:49:57 pm
i'm still confused...my calculator came up with "no solutions"

$\frac{1.35-\mu}{\sigma}=invNorm(0.15)= -1.036433$

$\frac{1.8-\mu}{\sigma}=invNorm(0.9)= 1.28155$

Solve simultaneous eq by hand or put in CAS, you get mean=1.55, sd=0.194
Title: Re: Normal distribution help!
Post by: JV-12 on October 14, 2012, 09:04:05 pm: thanks! i get it now :)