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# Simultaneous Equation watch

1. I've got the right values for Z but I cant seem to get the right answer when solving the simultaneous equations.

I got 0.2533 = (60000 - μ)/σ
which can be re arranged to make μ the subject:
60000 - 0.2533σ = μ
And then 1.282 = (50000 - μ)/σ which can be rearranged to:
1.282σ = 50000 - μ
As μ = 60000 - 0.2533σ I get:
1.282σ = 50000 -(60000 - 0.2533σ)
which if you expand you get:
1.282σ = 50000 - 60000 + 0.2533σ
= 1.0287σ = -10000 which isn't correct as you cant have a negative σ
Can anyone help me on where I went wrong?
2. (Original post by znx)

I've got the right values for Z but I cant seem to get the right answer when solving the simultaneous equations.

I got 0.2533 = (60000 - μ)/σ
which can be re arranged to make μ the subject:
60000 - 0.2533σ = μ
And then 1.282 = (50000 - μ)/σ which can be rearranged to:
1.282σ = 50000 - μ
As μ = 60000 - 0.2533σ I get:
1.282σ = 50000 -(60000 - 0.2533σ)
which if you expand you get:
1.282σ = 50000 - 60000 + 0.2533σ
= 1.0287σ = -10000 which isn't correct as you cant have a negative σ
Can anyone help me on where I went wrong?
The cumulative distribution for the Normal Distribution refers to the probabilities that P(Z<a) for some value a. However, you have a probability in the form of P(Y>50000)=0.9=P(Z>(50000-μ)/σ) and this must be converted into a probability of that form so that you have P(Z<(50000-μ)/σ)=1-P(Z>(50000-μ)/σ).
3. the value 50000 must lie to the left of the mean in order for 90% of the curve area to lie to the right. so you need to say 1.282 = (μ - 50000)/σ

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