Question: 1. A supplier makes packaging cartons for a customer, with a length normally distributed around a mean of 150mm. Due to the cavity in the

1. A supplier makes packaging cartons for a customer, with a length normally distributed around a mean of 150mm. Due to the cavity in the filling machine, the carton must be no longer than 157mm and no shorter than 143mm. The process standard deviation is 2.5mm. (a) What is the process capability Cp? Please keep 4 decimal places for your answer.

2. A sales completion team, aiming to reduce the shipment time of urgent orders, studies the current process and finds that the current shipment time has a mean of 4 days with a standard deviation of 1.5 days. Industry expectations are for urgent shipments to be delivered between 1 and 5 days. (a.) What is the current process capability Cpk? Please keep 4 decimal places for your answer.

(b.) One manager felt that the mean could be reduced to 3 days without changing the standard deviation. What is the process capability Cpk of the new system? Please keep 4 decimal places for your answer.

(c.) Another manager felt that the standard deviation could be reduced to 0.8 days without changing the mean. What is the process capability Cpk of the new system? Please keep 4 decimal places for your answer.

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