Question

Given a normal distribution, answer the following.

(a) What z-score forms the boundary between the highest 15% and the rest of the scores? z =

(b) What z-score forms the boundary between the highest 40% and the rest of the scores? z =

(c) What z-score forms the boundary between the lowest 20% and the rest of the scores? z =

(c) What z-score forms the boundary between the lowest 10% and the rest of the scores? z =

Answer 1

solution

(A)

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.04 ) = 0.85

z = 1.04

(using standard normal (Z) table )

B)

Using standard normal table,

P(Z > z) =40 %

= 1 - P(Z < z) = 0.40

= P(Z < z ) = 1 - 0.40

= P(Z < z ) = 0.60

= P(Z < 0.25 ) = 0.60  

z = 0.25 (using standard normal (Z) table )

(C)

Using standard normal table,

P(Z < z) = 20%

= P(Z < z) = 0.20

= P(Z <-0.84 ) = 0.20

z = -0.84 ( Using standard normal z table,

(D)

Using standard normal table,

P(Z < z) = 10%

= P(Z < z) = 0.10

= P(Z <-1.28 ) = 0.10

z = -1.28 ( Using standard normal z table,