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QUESTION

# For a normal distribution, mean u=8. Find standard deviation if r is the variable P(6&lt;r&lt;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