For a normal distribution, mean u=8. Find standard deviation if r is the variable P(6<r<10)=0.5 ?

The standard deviation is ##sigma=1.5##

The z-score is ##=(r-mu)/sigma##

Here we know.

##mu=8##

and ##P (6< r <10)=0.5 ##

Therefore, ##P(8< r <10)=0.25##

We look for the probability ##P=0.5## in the z-table

##z=0.67##

Therefore, ##(10-8)/sigma=0.67##

##sigma= 2/0.67=1.5##