Question

Determine the two​ z-scores that divide the area under the standard normal curve into a middle 0.19 area and two outside 0.405 areas.

Answer 1

SOLUTION:

From given data,

Determine the two​ z-scores that divide the area under the standard normal curve into a middle 0.19 area and two outside 0.405 areas.

The standard normal curve into a middle 0.19 area

Two outside 0.405 areas.

Find z such that P(-z < Z < z) = 0.19

=>  P(Z < -z or Z > z ) = 1-0.19

=>  P(Z < -z) + P( Z > z ) = 0.81

=> 2 *  P(Z < -z) =  0.81

=>P(Z < -z) =  0.81 / 2

=>P(Z < -z) = 0.405

In a z-table having area to the left of z, look for value closest to 0.405 inside the table, and find it along row named –0.2 and column named 0.03

Hence our answer is –0.23

P(-z < Z < z) = 0.19 = > z = –0.23 , 0.23