Drizzle is defined as precipitation consisting of very small water droplets (diameter less than 0.5 mm) that fall slowly and reduce visibility. It is produced by clouds with relatively shallow depth and small droplet sizes that cannot coalesce into full raindrops. 

Stratus and stratocumulus are the primary drizzle-producing clouds. Their shallow depth, stable internal structure, and small droplet size result in slow-falling fine water droplets that reach the surface as drizzle rather than rain. Stratus drizzle is particularly common in coastal and marine environments where moist stable air produces persistent low cloud.

Stratus or stratocumulus clouds → CORRECT. Stratus and stratocumulus are the classic drizzle-producing clouds. Their shallow depth and small droplet size produces the characteristic fine, persistent drizzle associated with overcast low cloud conditions. Stratus drizzle is a significant aviation hazard due to the reduction in visibility it causes.

Altocumulus clouds → INCORRECT. Altocumulus is a medium-level cloud family with bases typically above 6500 ft. Any precipitation falling from altocumulus generally evaporates before reaching the surface due to the dry air at lower levels (virga). Altocumulus does not typically produce surface drizzle.

Cirrus clouds → INCORRECT. Cirrus clouds are composed entirely of ice crystals and do not produce any precipitation at the surface. The ice crystals sublime back into water vapour as they fall into warmer drier air at lower altitudes. 

Cumulonimbus clouds → INCORRECT. Cumulonimbus produces heavy precipitation in the form of intense rain, hail, and sometimes snow. The precipitation from Cb is violent and convective, entirely different from the gentle light drizzle characteristic of stratus. Cumulonimbus also produces thunderstorms, lightning, and severe turbulence.