Problem #PRU-65300

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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?