Normal Distributions

alabama14

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Oct 30, 2011
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For a normal random variable X with a mean of 12 and a standard deviation of 3, find a number x0 such that the following probabilities are obtained:

a) P(X <= x0) = 0.5
b) P(X >= x0) = 0.23

My solutions:
a) To normalize X, I did (x0-12)/3 = 0 because the Z-value for 0.5 is 0. Solving for x0, I got x0 = 12.
b) Since X>= x0, I wasn't sure if you could solve the problem the same way as in part a. How would I solve part b?
 
That is impossible. Did you type the question correctly?

edit: These are two separate questions I am guessing. In that case a) is correct. For b, find the closest z-score corresponding to an area of 0.77 (it will be positive).
 
Last edited:
a) Why on Earth are you Normalizing ANYTHING?! This is an eyeball problem. Don't you dare calculate anything to answer this one.

P(Something from a Normal Distribution) = 0.50? Pick the Mean.
 
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