Gaussian Distribution for Probability

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Say I'm in a store, selling baubles. Each day, 100 people come to the store - each person has a 10% chance of buying a bauble. On average, 10 people will buy a bauble. But is there a gaussian distribution that models the chance of a given number of baubles being sold on each day? The mean would be 10, but would the standard deviation be? Is this an unsolvable problem?