I admit to lingering racism. Is it treatible?

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I would be the last person to think I am a racist. Yet I surprise myself when I apply racial stereotypes (in my mind) -- which, I assume, will translate into attitude and action. I was talking to a friend who is visiting here from Birmingham, England. I said, "In the old movies the Irish are portrayed as people who drink too much and get into fights. Is there any truth to that?" He says, "Yes. They are like that." Then I say, "The Scottish are portrayed as cheap (not just frugal) and independent cusses. Is that true?" "Yes," he said. "That's how they are." Then he asked, "From the movies I get the idea that Blacks are unable to control their emotions and are somewhat savage. Is that true?" I said, "I hope not." This conversation was disturbing... disturbing because I didn't say "NO" ...and disturbing for a lot of other reasons. I feel a bit of a moral failure because I've fought racism in myself. What are your thoughts? I'd like to learn from your opinion and observation.