This is the question with the correct answer below. How do you do this problem without having to refer to a distribution table? My midterm won't provide one so I can use it as reference, so I just want to know how to do problems like these without a table. Thanks!

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