# I am attempting to find an unknown value given the probability of the range of X. I am unsure of how to calculate the value given the added constants defined in the problem and which values I need to use to look up the z-scores to plug into the x = z + μ(σ). I have found z given probability of 0.95 to be 1.644853. Not really sure if that is the correct value to use or how to go from here? Here is the problem: A random variable X has the distribution N(1500,(200)^2). Find B, where P(1500−B<X<1500+B)=0.95

I am attempting to find an unknown value given the probability of the range of X. I am unsure of how to calculate the value given the added constants defined in the problem and which values I need to use to look up the z-scores to plug into the x = z + $\mu \left(\sigma \right)$. I have found z given probability of 0.95 to be 1.644853. Not really sure if that is the correct value to use or how to go from here? Here is the problem:
A random variable X has the distribution $N\left(1500,\left(200{\right)}^{2}\right)$. Find B, where $P\left(1500-B
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suponeriq
You can normalize the distribution and convert N(1500, 200^2) to N(0, 1):
P(1500-B < X < 1500+B) = 0.95
P(-B/200 < (X - 1500)/200 < B/200) = 0.95
Then you should be able to look up the value for B/200 in the table to find where
P(-B/200 < Z < B/200) = 0.95 where Z = $\frac{X-\mu }{\sigma }$ = N(0, 1).
Then you can solve for B by setting that value you found in the table equal to B/200.