You are told that X ($), the amount spent per patron at the Royal Brisbane show is normally distributed with mean $49.75 and standard deviation $13.60. Given this, answer the following questions:

a) Determine the probability that a randomly selected attendee spends more than $45 at the show. Show brief workings to support your answer.

b) Can we always use Z tables to determine probabilities associated with a particular variable of interest? Briefly explain the reasoning behind your answer.