If 20% of pea pods contain 80% of the peas, it is possible for the number of peas in a pod to be normally distributed?

To be honest, I’m not sure if the example in the title is very good. Instead of pea pods, have shoppers spending large amounts of money, and instead of peas, let that be the amount of money that they spend.

If the amount that any particular shopper spends follows a normal distribution, is it possible for 20% of the shoppers to spend 80% of the money?

To be even more specific, let’s say that the mean amount of money spent by a customer is $100. What would the standard deviation have to be in order for 20% of the shoppers to spend 80% of the money?

Assume that the store has a very, very large number of shoppers, and that spending follows a perfect normal distribution, regardless of practicality.