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?