Question

For a population with a mean of LaTeX: \muμ= 100 and a standard deviation of LaTeX: \sigmaσ=20, Find the X values that corresponds to each of the following z-scores: z = -.40 z = -.50 z= +1.80 z = +.75 z = +1.50

Answer 1

Population mean ( ) = 100

Standard deviation ( ) = 20

Formula for the z score is as follows

Z =  

Therefore

x = z + ---------(i)

Using this evaluation we can calculate the value of x.

1.For z = - 0.40

x = z +

= ( - 0.40 )( 20 ) + 100

= - 8 + 100

= 92

  x = 92

2. For z = - 0.50

x = ( - 0.50 ) ( 20 ) + 100

= - 10 + 100

= 90

x = 90

3. For z = + 1.80

x = ( 1.80) (20) +100

= 36 + 100

= 136

x = 136

4. For z = + 0.75

x = (0.75) (20) + 100

= 15 + 100

= 115

x = 115

5. For z = + 1.50

x = (1.50) (20) + 100

= 30 + 100

= 130

x = 130