Ok I posted this before, but the solution was given to me with use of a graphing calculator. For my midterm, I'm not going to be allowed to use a distribution table or a graphing calculator, so I'd like to know how to get the answer below the question without the use of either. Thank you very much for your help and for your time!!

Suppose a research rm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21? 0.9544