You need to decide how many shelving units to allocate to a certain product. The product comes in a box and you only can fit 10 of these boxes onto shelving unit. Shipments are following normal distribution. Mean 90 boxes/month, standard deviation 8 boxes/month. Boxes arrive during the first week of the month, and then are shipped the last three weeks of the month.
a) Whats the probability that 99 or more boxes arrive in 5 or more of the next 6 months?
b) whats the likelihood that more than 610 boxes arrive over a six month period?