Question

Find endpoint(s) on a N(0, 1) density with the given property.

(a) The area to the left of the endpoint is about 0.10.
(b) The area to the right of the endpoint is about 0.80.

(c) The area between ±z is about 0.95.

Answer 1

Solution,

Using standard normal table,

a) P( Z < z) = 0.10

= P( Z < -1.28) = 0.10

z = -1.28

b) P(Z > z) = 0.80

= 1 - P(Z < z) = 0.80  

= P(Z < z) = 1 - 0.80

= P(Z < z ) = 0.20

= P(Z < -0.84 ) = 0.20  

z = -0.84

P( -z < Z < z) = 0.95

= P(Z < z) - P(Z <-z ) = 0.95

= 2P(Z < z) - 1 = 0.95

= 2P(Z < z) = 1 + 0.95

= P(Z < z) = 1.95 / 2

= P(Z < z) = 0.975

= P(Z < 1.96 ) = 0.975

= z  ± 1.96