Suppose that the Dallas School District wants to achieve Six Sigma quality levels of performance in delivering students to school. They have 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? (Round your answer to 2 decimal places.) b. If they achieve this standard, about how many times out of a million deliveries will a bus deliver students either too early or too late? (Round your answer to 1 decimal place.)

a) 1.66 minutes

b) 3.4 out of million deliveries

Explanation:

So, it is a six sigma quality question, we first need to understand little bit about six sigma and how it is to achieve six sigma level.

Six Sigma:

It is the process or technique used by many organizations through out the world to achieve maximum quality in a product or in a service they are providing. It helps to indicate root causes of the process or you can say waste steps which first need to be identified then rectified to bring that top-notch quality in the system. So in this case, in order to calculate part a) we will calculate six sigma control limits.

a) So, for six sigma control limits, the maximum allowable standard deviation is 12 or you can say +6 + (-6) = ±6 = 12. It means all deviations must lie in all 12 standard deviations.

Please refer to the table shown in the attachment. This bell curve represent six sigma concept. In this 3 sigma quality level means all deviations must lie in 6 standard deviations.

So, here we have been given that mean = 20, so with mean we can calculate standard deviation in six sigma control limits.

Maximum Allowable Standard Deviation for 6 sigma = Mean/12

                                                                                        = 20/12

                                                                                       = 1.66

So, 1.66 is the maximum allowable standard deviation of arrival times required in order to achieve 6 sigma quality level.

b) In this part, we are asked that, out of million deliveries about how many times bus deliver students too early or too late at this 6 sigma quality level.

For this answer, please refer to attachment again. and notice at the left bottom with the arrow of 6 sigma, we have a number 3.4 ppm means 3.4 part per million.

So, it 3.4 times in a million deliveries bus will deliver students either too early or too late.