Question

(1 point) Use Table A to find the proportion of the standard Normal distribution that satisfies each of the following statements.  
(a)z<0.15 (b)z>0.15 (c)z>−2.82 (d)−2.82<z<0.15

Answer 1

Part a

Z =0.15                              

Using Z table we get

P( Z < 0.15 ) = 0.5596

Proportion is 0.5596

(Check the 0.1 row and 0.05 coulme in the Z table to get proportion)

part B

P( Z > 0.15 ) = 1- 0.5596 = 0.4404

P( Z > 0.15 ) =0.4404

( Z table gives proportion for < sign but we have > sign and taotal proportion is 1.

so we did P( Z > z ) = 1- P( Z< =z)   )

Part C .

P( Z > -2.82 ) = 1 - P( Z < = -2. 82 )

                      = 1 - 0.0024

                      = 0.9976

P( Z > -2.82 ) = 0.9976

( Using negative value table Check -2.8 row and 0.02 column to get 0.0024)

Part D.

P( -2.82 < Z < 0.15) = P( Z < 0.15) - P( Z < -2.82)

                                 = 0.5596 - 0.0024 = 0.5572              ( Using part a and c)

P( -2.82 < Z < 0.15) = 0.5572

Using below table you can find proportion .