The City of Someville is planning to build a commuter train to run along Main Street. Someville is a one-street town – all its population lives on Main street, and it is distributed approximately according to a Normal distribution centered on the center of the town. The city government has enough money to build 5 train stops. Every station will service the people closest to it. (To clarify this point, suppose that Main Street runs in a straight line East-West, so that the station furthest West services every person who lives West of it, as well as those to the East of it who live closer to it than to the next station. Similarly, the station furthest East services everyone who lives East of it, as well as everyone who lives West of it and closer to it than to the next station. The other stations service everyone who lives up to halfway toward the next closest station in either direction).
If each stop is to service the same number of Someville inhabitants, where should each station be located along main street, in relation to the center of town?
I think it has something to do with standardizing and z scores. Could someone help out? Thanks