After years of practicing at the loual zoom in bowling alley, Allan has determined that his distribution of bowling scores is roughly symmetric, unimodal, and bell-shaped, with a mean of 182 points and a standard deviation of 23 points. How likely is it that Allan will roll a perfect game (300 points), just by random chance? Explain. The probability of Allan rolling a perfect game by random chance is likely because that score is within 3 standard deviations of the mean. The probability of Allan rolling a perfect game by random chance is not very likely because that score is more than 3 standard deviations from the mean