Question on Normal Distribution problem

#1
Problem:
Suppose the average age in a certain country is 30.5 years, with a std. dev. of 8 years.

Question:
38% of the pop. has ages between A and B. A's age is 38.5 and is older than B. How old is B?

My work:
38.5-30.5/8 = 8/8 = 1 = .8413
.8413-.38 = .4613

X-30.5/8 = ?
I am stuck on figureing out X
what do I need to do to figure out the rest of the problem and figure out B's age?
My friend got the answer 29.7 years not sure how to get there.
 

Dragan

Super Moderator
#2
My friend got the answer 29.7 years not sure how to get there.

Your friend is correct.

That is, obtain the corresponding Z-value that yields a cumulative proportion of 0.4613 i.e. Z = -0.0970458.

Subsequently solving for B (or X as you called it) yields:

B = Z*Std + Mu or

B = (-0.0970458)*8 + 30.5 = 29.72...