Suppose you work at the Wesco distribution center in Cranberry and you are the Industrial Engineer in charge of operations. You need to decide how many shelving unit storage locations to allocate to an electronic switchbox. The switchbox comes in a cardboard carton and you can fit 10 of these cartons onto one shelving unit. Currently shipments arrive following a Normal distribution with a mean of 80 cartons per month and a standard deviation of 7 cartons per month. Assume that the switchboxes arrive during the first week of the month and then are shipped out during the last three weeks of the month.

What is the likelihood that more than 510 switchboxes arrive over a six month period?

What is the likelihood that more than 510 switchboxes arrive over a six month period?