Normal distribution ( Gaussian )

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Warthogger

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Normal distribution problem ( Gaussian )

Hi I've managed well so far but I've come across a problem I'm unaware how to apply the Z score to.

The problem is.

The Life of a machine component is normally distributed with mean 60 hours and standard deviation 30 minutes. If 2.5% of components last more than X1 hours, find the value of X1.

X = ? not sure how to work it out or how to rearrange the formula with out been given Z value or X
mu = 60
Std Dev = 30

So i did 2.5% as 0.5 - 0.025 to get the area remaining from 0 - Z1 which = .4975 and found that value on the z chart to find the value of Z.

I then used the formula x=Mu+(Z)(Sigma) and got

60+(2.8*30) = 144 so am i right in saying X = 144?

any advice would be appreciated.
 
Last edited:
Warthogger said:
Hi I've managed well so far but I've come across a problem I'm unaware how to apply the Z score to.

The problem is.

The Life of a machine component is normally distributed with mean 60 hours and standard deviation 30 minutes. If 2.5% of components last more than X1 hours, find the value of X1.

X = ? not sure how to work it out or how to rearrange the formula with out been given Z value or X
mu = 60
Std Dev = 30

So i did 2.5% as 0.5 - 0.025 to get the area remaining from 0 - Z1 which = .4975 and found that value on the z chart to find the value of Z.

I then used the formula x=Mu+(Z)(Sigma) and got

60+(2.8*30) = 144 so am i right in saying X = 144?

any advice would be appreciated.
Click to expand...
How large is z when the upper tail of the distribution is 2.5%? You are NOT 2.5% away from the mean, but just 2.5% shy of the full area of the distribution.
F = 1 - 0.025 = 0.975
z = 1.96

Then use the formula to get the X1 that corresponds to z=1.96
 
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