Costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $74 and a standard deviation of $22. what is the probability that one bill for veterinary services costs between $41 and $107?

The probability is 0.8664.

The formula for z-scores is

z = (X-μ)/σ

The z-score for the lower limit is
z = (41-74)/22 = -1.5

The z-score for the upper limit is 
z = (107-74)/22 = 1.5

Using a z-table (http://www.z-table.com) we see that the area to the left of the lower limit is 0.0668.  The area to the left of the upper limit is 0.9332.  The area between them is found by subtraction:

0.9332-0.0668=0.8664.