Using the standard normal distributton, find the two z-scores that that form the middle shaded region, Theshaded region is symmetric about z 0. Round your z-scores to two decimal places.Shaded Area-0.32-30.

Answered: Using the standard normal distributon,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Using the standard normal distributton, find the two z-scores that that form the middle shaded region, The
shaded region is symmetric about z 0. Round your z-scores to two decimal places.
Shaded Area-0.32
-3
0.

Expert Solution

Step 1

Given

The shaded area=0.32 and

The shaded region is symmetric about z=0.

That is the shaded region above the point zero is 0.16 and below the point zero is 0.16 .

Suppose the two z-scores that form the middle shaded region are $z_{s c o r e} a n d - z_{s c o r e}$ .

$P (Z < 0) = P (Z > 0) = 0.5 (\sin c e d i s t r i b u t i o n s y m m e t r i c a b o u t z = 0) T h e r e f o r e P (Z < z_{s c o r e}) = 0.5 + 0.16 = 0.66$

Step 2

$T h e z - s c o r e i s : P (Z < z_{s c o r e}) = 0.66 P (Z > z_{s c o r e}) = 1 - 0.66 P (Z > z_{s c o r e}) = 0.34 b y u \sin g n o r m a l p r o b a b i l i t y t a b l e, w e g e t z_{s c o r e} = 0.41$

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