Question

The area under the standard normal curve from zero to z is 0.29. The value of the z-score could be:

Answer 1

The area under the standard normal curve from zero to z is 0.29.

To find value of the z-score

Now we are given that

P ( 0 Z z ) = 0.29

P( Z z ) - P (Z < 0 ) = 0.28

Now P(Z <0 ) = 0.5

Thus ,

P( Z z ) = P (Z < 0 ) + 0.28

P( Z z ) = 0.5 + 0.28

P( Z z ) = 0.78

Thus we need to find z , we will R -software to obtain value of z

> qnorm(0.78,0,1)            
[1] 0.7721932

Thus z = 0.7721932

Hence

P(Z z ) = P(Z 0.7721932 )   = 0.78

Also

P( 0 < Z < 0.7721932 ) = P( Z 0.7721932) - P (Z < 0 )

                                     = 0.78 - 0.5

P( 0 < Z < 0.7721932 ) = 0.28

Hence The value of the z-score could be: 0.7721932 0.7722

The shaded area between 0 to 0.7722 is 0.28