You're final solution looks correct to me but you forgot the 7!/(3!4!) constant out front when you were deriving the answer.

An easier way to do problems like these is to find the probability of getting the complement of what you want ( 10<x<14 ) and then we know that if A and A' are complements then P(A) = 1 - P(A')d.I have no idea how to deal with this one

I think I have to use the mean and standard deviation of the problem

(µ=12, =2)

P(x<10) or P(x>14)

Hope you people can help me