Suppose that the Dallas School District wants to achieve Six Sigma quality levels of performance in delivering students to school. It has established a 20-minute window as an acceptable range within which buses carrying students should arrive at school. 

a. What is the maximum allowable standard deviation of arrival times required in order to achieve this standard of quality?

b. If the school district achieves this standard, about how many times out of a million deliveries will a bus deliver students either too early or too late?