The mean height is 165cm, the standard deviation is 5cm, and the LSL is 162.5cm. There is no other information or data. If we assume that the population is normally distributed, how can we calculate the cumulative probability?

[#1]

You can assume that the data is normally distributed and then plot the data with this assumption.
With probit scale, this is just a straight line - without any structure.

But in real life, what you want to do with a cumulative distribution is actually the opposite of this: 
check for deviations. Without having the data at hand, this is not possible.

[#2]

Hi @FairAlpaca11785 : Is this a homework problem?