How to find mean and deviation of the following samples?

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We have the following problem where
X: "Height of a plant" follows normal distribution.
$$ P(x<68) = 0.025 $$ $$ P(72<=x<=68) = 0.475 $$ $$ P(x>72) = 0.5 $$

How to find P(60<=x<=70)?
Do I have to find mean and deviation and then use z-table or there's something more clear?


Note. If I had discrete values for example:
P(x=1) = 0.025
P(x=2) = 0.475
P(x=3) = 0.5
Then $$μ_χ=0.025*1 +0.475*2+0.5*3=2.475$$ $$σ_χ=(1-2.475)^2*0.025+(2-2.475)^2*0.475+(3-2.475)^2*0.5=0.299375$$ Then using the z-table I could calculate P(x>2.5)

How can I calculate mean and deviation for the continuous values above?