Question

Use the given shaded area (0.2549) in the middle of the standard normal distribution and the given z-score (-1.14) to find the missing z-score. The shaded region is not symmetric about

z

=

0

z

=

0

. Round your final answer to two decimal places.

-4

-3

-2

-1

0

1

2

3

4

z

Shaded Area = 0.2549

-1.14

?

Upper z-score =

Answer 1

solution:

Given data

Z is a standard normal distribution table and it is not symmetric about - { -4,-3,-2,-1,0,1,2,3,4}

  P(-1.14 < Z < Z1) = 0.2549

P(Z<Z1) - P(Z<-1.14) = 0.2549

P(Z<Z1) = 0.2549+ P(Z<-1.14)

P(Z<Z1) = 0.2549+P(Z>1.14)

= 0.2549+ [ 1 - P(Z<=1.14) ]

= 1.2549-P(Z<=1.14)

= 1.2549 - 0.8729 [using standard normal distribution table ]

P(Z<Z1) = 0.3820

Z1 = -0.3002

Z1 =~ - 0.30

So, P(-1.14 < Z < -0.30) = 0.2549

Upper z-score = -0.30