Laboratory (GRAIL) spacecraft "Ebb" and "Flow" whose purpose was to perform gravitational field mapping of the Moon to determine its interior structure. The primary phase of the mission was planned to last approximately 90 days, after which the spacecraft would be powered down, decommissioned and crash-landed on the moon. NASA used lithium-ion (Li-ion) batteries to power the spacecraft, which have a mean time between failure in a space environment of 30 days. Because it was critical to accomplish the full duration of the mission, NASA designers knew they had to include a number of backup batteries on each spacecraft. However, to save cost and fuel they needed to minimize the number of batteries. Spacecraft battery template a) Using a Weibull distribution with a=1 and =30 what is the probability that one battery will last for the entire mission? b) What is the minimum number of batteries required to assure with 95% confidence that a spacecraft will successfully complete its mission? c) How many batteries would be required (assuming 95\% confidence) if the mission were extended to by 90 days