5. Problems for Section 5.4: Statis 1. (*) Tyler Apiaries sells bees and beekeeping supplies. Bees (including a queen) are shipped in special packages accord- ing to weight. The target weight of a package is 1.4 kg. Historically, Tyler's shipments have weighed on average 1.4 kg, with a standard deviation of 0.15 kg. a. (*) Calculate the process capability ratio, assuming that the lower and upper tolerance limits are 1.1 kg and 1.7 kg, respectively. Is Tyler Apiaries currently able to meet the tolerance limits 99.7% of the time? b. (**) What would the standard deviation have to be for Tyler Apiaries to achieve Six Sigma quality levels with regard to the weight of the bee packages? c. (**) The average bee weighs 0.1 grams. Use this infor- mation to convert the target package weight and tolerance limits into number of bees for Tyler Api- aries. How might the company use this information to better control the package weights? Should Tyler Apiaries think about resetting the tolerance limits? 2. (*) Tyler Apiaries sells bees and beekeeping supplies. Bees (including a queen) are shipped in special packages according to weight. Suppose Tyler changes its processes so that the average package weight is now 1.5 kg, with a new standard deviation of 0.2 kg. Tyler markets the pack- ages of bees as weighing 1.4 kg, and the tolerance limits remain as before. Calculate the process capability index for the weight of the bee packages. Is Tyler able to meet the tolerance limits