Problem #PRU-65300

Problem

A sailor can only serve on a submarine if their height does not exceed 168 cm. There are four teams $A$, $B$, $C$ and $D$. All sailors in these teams want to serve on a submarine and have been rigorously selected. There remains the last selection round – for height.

In team $A$, the average height of sailors is 166 cm.

In team $B$, the median height of the sailors is 167 cm.

In team $C$, the tallest sailor has a height of 169 cm.

In team $D$, the mode of the height of the sailors is 167 cm.

In which team, can at least half of the sailors definitely serve on the submarine?