For X~N (105,16), then what percent of the data are contained in the interval 97-105?

I need help getting started on this question...up to the point where I have to calculate the z-scores and I'll take it from there.

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- October 28th 2008, 05:51 PMperronpercentage of interval
For X~N (105,16), then what percent of the data are contained in the interval 97-105?

I need help getting started on this question...up to the point where I have to calculate the z-scores and I'll take it from there. - November 1st 2008, 12:59 AMAngelAngel (Best Solution)
X~N (105, 16)

Compare the given form with general form,

So,

X~N (105, 16) Compare to X~N (µ, σ2 )

After comparing we get,

µ=105

σ=4

We have to find the interval from X=97 to X=105.

When X=97 then

Z= (97-105)/4

Z=-2

When X=105 then Z will be 0 because this is mean.

So we have to find interval between Z=-2 to Z=0

P (between Z=-2 to Z=0)=0.4772 required answer