Compute the following probabilities: A. If Y is distributed N (-8,9), Pr (Y≤-12) = —— . (Round your response to four decimal places.)
B. If Y is distributed N (-4,9), Pr (Y>-1) = ——. (Round your response to four decimal places.)
C. If Y is distributed N (40,25), Pr (34≤Y≤44) = ——. (Round your response to four decimal places.)
D. If Y is distributed N (−3,4), Pr (Y>−4) = (Round your response to four decimal places.)

a) P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b) P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c) P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d) P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

Step-by-step explanation:

Normal Distribution:   N ( -8 ; 9 )

a) P [ Y ≤ -12 ]  = ( - 12  - (-8))/9

P [ Y ≤ -12 ]  =  - 4/9  = - 0,44

From  z-table for the z score -0,44 we get:

P [ Y ≤ -12 ]  =  0,32997      or        P [ Y ≤ -12 ]  = 32,99 %

b)  Normal Distribution:   N ( - 4 ; 9 )

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]

P [ Y ≤ -1 ]  =  ( - 1 - ( - 4 ) ) / 9

P [ Y ≤ -1 ]  =  3 / 9  =  0,3333

From  z-table for the z score 0,33 we get:

P [ Y ≤ -1 ]  = 0,6293

P [ Y > -1 ]  =  1  - P [ Y ≤ -1 ]  =  1 - 0,6293

P [ Y > -1 ]  =  0,3707          or   P [ Y > -1 ]  =  37,07 %

c)  Normal Distribution:   N ( 40  ;  25  )

P [ 34 ≤  Y  ≤  44]

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

 P [  Y  ≤  44]  = ( 44 - 40 ) / 25   = 0,16

From  z-table for the z score 0,16 we get:

P [  Y  ≤  44]  = 0,5636

P [ Y ≤ 34 ]  = ( 34  - 40 ) / 25   =  - 6 / 25   = -  0,24

From  z-table for the z score -0,24 we get:

P [ Y ≤ 34 ]  = 0,40517

Then

P [ 34 ≤  Y  ≤  44]    = P [  Y  ≤  44]  -  P [ Y ≤ 34 ]

P [ 34 ≤  Y  ≤  44]    =   0,5636 -  0,40517

P [ 34 ≤  Y  ≤  44]    =  0,1585      or     P [ 34 ≤  Y  ≤  44]    =  15,85 %

d)  Normal Distribution:   N ( -3  ;  4  )

P [ Y > -4 ]  =  1  -  P [ Y ≤ -4 ]

P [ Y ≤ -4 ]  =  ( - 4 - ( -3))/4  =  - 1/4  = - 0,25

From  z-table for the z score -0,25 we get:

P [ Y ≤ -4 ]  = 0,40129

P [ Y > -4 ]  =  1  -  0,40129

P [ Y > -4 ]  = 0,59871         or        P [ Y > -4 ]  = 59,87 %

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