Forget about whether this is useful to a programmer. I find this basic statistics knowledge so indispensable that I don't understand why it's not taught in dumbed-down form (i.e. without calculus) in high school. Learning these concepts can be useful in data mining/machine learning fields, since this field is arguably the intersection of statistics and computer science. Even if you never do any data mining, understanding basic statistical concepts will make it easier for you to interpret things like performance benchmarks. It could even be useful for understanding things like Web server load. The number of users signed on can be modeled as a random variable with a Poisson distribution, though the Poisson parameter may vary by time of day.
Also, I generally think that, within reason, it's better to focus on breadth rather than depth as an undergrad. The chances of you remembering and using the exact details of what you learn after you graduate are pretty slim. The chances of you using the general principles you learn in some capacity or another are very high. Secondly, no matter what you think you're going to be doing after you graduate, you'll probably deviate somewhat from that plan. Even more importantly, you can easily learn more about a field after you already know the basics, but it's tough to know you need to learn more about a field that you barely know exists. Therefore, it pays to learn the fundamentals of a lot of related fields, such as math, physics, statistics, engineering, etc. more than to go into a ton of depth about a narrow area.
Disclaimer: I work in bioinformatics, which is basically the intersection between molecular biology, statistics and computer science, so of course I like statistics and think it's important.