Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs exactly 185 pounds?
Why the answer is 0?
Because weight is a continuous variable (a variable that can has any value within an interval). If probability is expressed as favorable cases / possible cases, there is 1 possible case (weight is exactly 185 pounds) versus infinite cases (weight is any other value, and there is infinite values within an interval)
For a Gaussian distribution, it makes more sense to ask which is the proability for a man's weight to be lower or greater than a certain value.