A chain of stores knows that 90\%90%90, percent of its customers pay with a credit or debit card, 5\%5%5, percent pay with cash, and 5\%5%5, percent pay with a service on their smartphones. They installed a new system for receiving payments, and they wonder if these percentages still hold true. They plan to take a random sample of customers in order to perform a \chi^2χ 2
\chi, squared goodness-of-fit test on the results.
What is the smallest sample size the company can take to pass the large counts condition?