Please translate the following into standard normal probability distribution

Question

(transform x to z) with Mean μ = 30 and standard deviation σ = 4. Find P(x < 40) ; P(x > 21) ; P(30 < x < 35)

Answer 1

 

Hi Leva,

 

The formula for the transform is z = (x - μ)/σ.

 

So,

 

     P(X < 40) = P(Z < (40-30)/4)

 

                    = P(Z < 2.5)

 

     P(X > 21) = P(Z > (21-30)/4)

 

                    = P(Z > -2.25)

 

     P(30 < X < 35) = P((30-30)/4 < Z < (35-30)/4)

 

                            = P(0 < Z < 1.25)

 

Hope these help.