X is normally distributed with mean where the mean is greater than zero

If

what is the closest decimal approximation for the value

???

a:0.025

b:0.05

c:0.475

d:0.4875

e:-0.025 (obviously wrong choice, just provided for question completeness)

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- September 5th 2011, 03:31 AMIstafaDifficult Normal Distribution question
X is normally distributed with mean where the mean is greater than zero

If

what is the closest decimal approximation for the value

???

a:0.025

b:0.05

c:0.475

d:0.4875

e:-0.025 (obviously wrong choice, just provided for question completeness) - September 5th 2011, 04:37 AMSironRe: Difficult Normal Distribution question
I would rewrite the probability:

- September 5th 2011, 04:45 AMIstafaRe: Difficult Normal Distribution question
This looks like a good approach, except how do I find Pr(x<-a)? Pr(X< mu) is obviously 0.5, but this alone doesn't allow me to solve the question...?

Thanks in advance. - September 5th 2011, 04:53 AMSironRe: Difficult Normal Distribution question
Notice

- September 5th 2011, 05:01 AMIstafaRe: Difficult Normal Distribution question
This approach gives the answer as c above, but how does P(x<-a)=P(x>a) hold true even when mean is not zero?

- September 5th 2011, 05:06 AMSironRe: Difficult Normal Distribution question
Because the graph of normal distribution is symmetric.

- September 6th 2011, 03:57 AMIstafaRe: Difficult Normal Distribution question
*Symmetric about the mean*, hence P(X<mu-b) would be equal to P(X>mu+b) for any b but if mu is not zero then P(x<-b) would not equal P(x>b) for an b. Or is there a flaw in this logic? Hmmm...