At what temperature CO2 becomes solid at normal pressure?
The phase diagram you have shown is correct and shows the sublimation point at $1~\mathrm{atm}$ as $-78.5~\mathrm{^\circ C}$ . So if you have a pure $\ce{CO2}$ atmosphere, it will solidify at $-78.5~\mathrm{^\circ C}$.

Temperatues in Antarctica are known to get below $-78.5~\mathrm{^\circ C}$ so you might wonder why whe don't find dry ice in Antartica (like we do at the Martian poles [Note: they are a lot colder]). The reason is that the partial pressure of $\ce{CO2}$ in the atmosphere is so low that at $-78.5~\mathrm{^\circ C}$, dry ice is forming but it is subliming faster than it forms because the vapor pressure of $\ce{CO2}$ in the atmosphere above it is well below the saturation vapor pressure required for ice to accumulate.


  The vapor pressure must reach the saturation vapor pressure for dew or frost to form. This happens at the dew point or frost point temperature, which is dependent on atmospheric pressure and the absolute amount of vapor in the air. As atmospheric temperature increases, the dew/frost point temperature increases. As atmospheric pressure increases, the vapor pressure increases. At very low temperatures, the dew/frost point temperature is very low.


http://wattsupwiththat.com/2009/06/13/results-lab-experiment-regarding-co2-snow-in-antarctica-at-113%C2%B0f-80-5%C2%B0c-not-possible/

https://stevengoddard.wordpress.com/2014/06/03/antarctica-gets-cold-enough-to-freeze-co2/