QM - Normalising percentage, copyright, question, standard, average

prav_Cfa7

Hey Guys I came across this question in a third party prep provider. I have changed the question around to avoid copyright violations.

"The percentage changes in annual earnings for a company are approximately normally distributed with a mean of 5% and a standard deviation of 12%. The probability that the average change in earnings over the next five years will be greater than 15.5% is closest to:

a) 10%
b) 2.5%
c) 5.0%

Answer:
B

The first time I attempted this question I firstly tried to normalise it the ordinary way.

15.5-5/12

However looking at the answers you need to divide the numerator by the standard error. Can somebody explain to me why this is so and how you can differentiate a ordinary normalising question from one such as this? Was the "over the next 5 years" part of the question the give away?

Thanks