Wendy's fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 500 and standard deviation of 90 and the demand for chicken sandwiches is normally distributed with a mean of 150 and standard deviation of 30. Use this information to answer the following questions.
If the restaurant stocks 550 hamburgers and 160 chicken sandwiches for a given day, what is the probability that it will run out of neither hamburgers nor chicken sandwiches that day? Assume that the demands for hamburgers and chicken sandwiches are probabilistically independent.