To determine whether it's appropriate to use the normal approximation, you need to check if the conditions for a normal approximation are met. Usually, these conditions include a sufficiently large sample size and the presence of a reasonably symmetric distribution.
If your sample size is large enough (typically greater than 30) and the data are not heavily skewed, you can use the normal approximation to estimate probabilities. However, without knowing the specific sample size and distribution shape in your scenario, I can't give a definitive answer. Please provide the sample size, and if possible, information about the distribution of the data for a more accurate assessment.