A height of 6 feet 2 inches is approximately the 95th percentile for adult male height in the United States.
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The Short Version
The claim is well supported by U.S. anthropometric data. CDC/NCHS NHANES references place the 95th percentile for adult U.S. men at about 187.3-187.5 cm, while some related analyses put it near 188 cm. Since 6'2" equals 188.0 cm, describing it as approximately the 95th percentile is accurate.
Caveats
The exact 95th-percentile cutoff in recent CDC tables is slightly below 6'2"—about 187.5 cm rather than 188.0 cm.
This applies to U.S. adult men overall, not necessarily to specific age bands, racial/ethnic groups, or younger males.
Measured NHANES data are the strongest basis here; self-reported height sources can slightly overstate height percentiles.