The normal distribution is really important in statistics, but it can be tough to deal with for a few reasons:

1. Central Limit Theorem (CLT): This rule says that when we take averages from samples, they tend to look like a normal distribution, even if the original data doesn’t. But this can be slow and tricky, especially when we have small samples.

2. Assumptions: Many statistical methods assume that the data is normal. If the data isn’t normal, we can get wrong results. This is especially true in hypothesis testing, where we might make Type I or Type II errors.

3. Real-world applications: In the real world, data often doesn't fit the normal pattern. This can make it hard to use standard statistics techniques.

Possible Solutions:

• We can test for normality using tools like the Shapiro-Wilk test.
• We can change the data using transformations, like taking the log or square root, to make it more normal.
• We can choose non-parametric methods that don’t need these normality assumptions, which can make our results more reliable.